I intend for this to complement, not replace, what Sam said.
There are many, many types of weapons used by a variety of soldiers in the medieval era (although the 15th century is more of the Renaissance-era), designed for various purposes. I will attempt to cover the major ones.
As Sam said, these weapons include maces, mauls, war-hammers, and other weapons designed to deal impact damage to bones and tissue without penetrating armor. You won't likely see any use of your ultra-light high-strength metal (which is less dense even than titanium). These weapons rely on momentum for their damage potential and require significant mass.
You might possibly see your lighter metal in maul chains to allow for more of the overall mass of the weapon to be concentrated in the end.
There are some advantages to lighter edged weapons, again as Sam said. Faster movements allow for better targeting of the moving openings in armor and improved slashing attacks. Off-hand weapons like parrying daggers (though not really used on the battlefield) would also benefit from being lighter, allowing better protection and faster parrying.
Personally, I think thrusting weapons (mostly thrusting swords) have the biggest advantage in being lighter without sacrificing strength, as it allows you to impart more force in the thrust, improving penetration of mail and the underlying tissue.
You won't likely see much use in ranged weapons, except perhaps in the previously steel parts of crossbows. Those, however, are peasant weapons and it's unlikely a noble would spend extra money to outfit his peasants with lighter crossbows. Crossbow bolts and arrows rely on momentum for their penetration - too light of an arrow won't penetrate the target, so those are off the table.
Early firearms might benefit from a light, strong material like yours, but those early projectiles likewise depended on their mass to do damage.
Polearms, again, are peasant weapons. Though they would benefit somewhat from lighter heads, that's not going to offset the generally very heavy wooden pole.
Given the overall rarity of your wonder-steel, the weapons made will likely be restricted to nobles and perhaps their personal guard. The bulk of armies, which were generally peasants, were outfitted with cheap arms and drew strength from numbers and strategies (and having more people than the other guy).
TL;DR - Overall, I believe your material is more likely to impact duels among nobility than it is large-scale warfare.