I would say a diplomat's weapon should be multi-purpose; not only a deadly tool for killing, but an attractive status piece that could reflect well on their hosts. Weapons aren't completely prohibited of diplomats, and few but the most paranoid of rulers would seize each and every one of their visitors' weapons. Take this portrait of Moroccan ambassador to England ‘Abd al-Wāḥid ben Mas‘ūd from 1600. Note his very attractive sword displayed for all to see.
Here's a breakdown of my ideas:
Deadly, attractive, and lightweight. They don't hold exceptionally well against anything except another rapier, though, due to the skinny blade that can easily be cracked by a strong hit from a larger weapon, like an axe or club. Intended for gentlemanly duels and finding an unintentional nieche as a capable tool for assassins, but it cannot hold its own in prolonged combat and is unlikely to cause real damage in an emergency to anything more serious than an angry deer.
Lethality: As a dueling weapon, they are intended to cause only superficial injuries, not lethal ones. As a sword, however, they are just as capable of murder as any other sharpened metal. The thin blade is especially well-designed for silent assassinations and decisive hits at vital points, especially into the neck from beneath a helmet.
Disabling: The rapier is designed to parry. A strong enough slice with it could likely even slice through the shaft of a spear, at some considerable risk to the blade.
Concealing: They are not made to be concealed, they are made to be paraded about and draw attention with their immaculate design - though by trading the basket hilt for a small crossguard and possibly even a shorter blade, they could be hidden under a long coat - but they are really not designed to be concealed.
Distancing: Maintaining distance from your opponent is the first rule of dueling. The long blade can keep an opponent at bay and the exceptionally light weight can facilitate quick movements even while drawn.
Range: No. They are too light and the handle too heavy on its own. How dare you even think to toss such a magnificent design??
Attractiveness: That is the whole point, dear. Their large, decorated basket hilts are the epitome of elegance and utility. Many rapiers of the world never drew blood, and existed solely because of their supremely attractive design.
Lethal, lightweight, and stealthy. A small hand-axe could be a solid choice. It can break a wood shield, chop the head off a spear, or kill someone very quickly with a well-placed blow. Especially with monsters, the extra swing force could help with thick hides or bony plates.
Lethality: It's actually quite hard not to kill someone in the case of axes, though there are some axes that have a blunt end on the opposite side of the blade, which could be used for less lethal attacks.
Disabling: Chopping off a few choice fingers will reduce the capability of any opponent. They're not as gifted as swords when it comes to parrying long blades, but they can hack the business end off a spear with relative ease if you're quick about it.
Concealing: A one-handed axe can easily be hidden away beneath a long coat.
Distancing: You have to be practically kissing your enemy to get any use out of an axe.
Range: You can throw an axe, but your accuracy has to be on point if you're using one that has the hybrid intent of crushing blows and deadly throws. Smaller, often square-shaped axe heads intended for throwing lose much of the weight and blade area
Attractiveness: Though they can be impressively decorated, the utilitarian design of the axe leaves precious little to the imagination. Without this expensive decoration, they are relatively unattractive things. Axes also tend to carry a connotation of barbarism in most courts, which could leave a poor impression.
Lightweight, attractive, and stealthy. As you had already said, though, they are intended for nothing short of quick and seamless lethality, and they are not made to parry or disarm and cannot keep enemies at bay with any ease.
Lethality: The intention of a dagger is to kill. Your best bet for non-lethality is to leave superficial wounds until your opponents surrender, and even then, that's a lot of blood loss. We're already asking our ambassadors to be experienced combatants and skilled diplomats - adding medical training into the equation is probably asking too much.
Disabling: Not facilitated by the dagger's design. Your best bet is agility here.
Concealing: Daggers are famously easy to conceal. You can hide them basically anywhere.
Distancing: Daggers are small. Not a strength of theirs.
Range: Not made to be thrown, actually. They're balanced for quick, stabbing blows and most would serve about as well as a rapier if thrown. Throwing knives are even smaller, lighter, and less effective in prolonged combat.
Attractiveness: Daggers are often extremely attractive with little effort. Even without extensive decoration, the long shiny blade is a certainly beautiful thing. Similarly to the axe, however, they carry a connotation of assassins and thieves in most places, and might leave a negative impression in some courts.
Lethal, lightweight, attractive, and stealthy. Essentially a short sword, but intended for dagger-like use. The long, sharp blade could stab deep into the heart of a beast, and the attractive traditional designs are sure to impress. Keep in mind that this is, however, my favorite bladed weapon on the planet and in that I may be slightly biased.
Lethality: It is a sword, it is made to kill. Like the other long-bladed weapons mentioned, they are hard-pressed to not leave fatal wounds.
Disabling: It can parry, though not quite as well as a longer weapon. Disarming is not it's forte.
Concealing: Effective like a sword, stealthy like a dagger. A khanjali can be hidden almost anywhere, especially with a larger coat.
Distancing: It is a blade, and so you will have to hit them with it. They are made for stabbing as well, and not slashing, so you must get even closer.
Range: Like most melee weapons, they are not made to be thrown and you'd need to be exceptionally lucky to hit anyone with it.
Attractiveness: Absolutely. They are traditionally very beautiful things. Displaying such a fine weapon is sure to inspire equal parts respect and envy anywhere.
I have seen several diagrams and still I don't fully understand how these are supposed to work, but regardless, it's probably the best fit for the rules set here. An accessory, whip, and sword in one tool.
Lethality: As a sword, it is undeniably lethal like any other blade. As a whip, it can take off a limb in a single move, or disable an enemy with ease with its sharp edges and inherent damages of cracking a whip.
Disabling: You could literally whip the weapon out of their hand. Excells in this regard.
Concealing: Who would suspect a belt?
Distancing: Whips can cover quite a lot of distance. Excells in this regard.
Range: Can't be realistically thrown, but the whip itself covers a considerable distance.
Attractiveness: What an accessory! As it's mostly blade, it may not be very wise to decorate the most of it, but it still is rather stunning.