disintegrates anything caught by the beam into basic atoms and molecules
Yep, seems feasible...
with no wound or gash, more as if a portion of the targeted material or person simply ceased to exist.
that's a bit of a bigger ask...
no utter handwavium (no fictional physics).
...aaaaaand that just about puts the nails in the coffin of that idea.
You just can't vanish stuff. You can transmute it into other things which either leave the area of effect promptly or are rather hard to see, but those things are exceptionally dangerous.
As a very quick and dirty baseline figure, consider that an "average" adult human weighs ~62kg and is perhaps 65% water. It takes about 11MJ to raise that to boiling point, and then a further 91MJ to turn it to steam. That steam with have an initial pressure of the order of 46MPa, which is quite a lot higher than atmospheric pressure... that means it will expand. Rapidly. Boom. Meat BLEVE. And that's just boiling the water without worrying about any other materials or even breaking any chemical bonds. If you wanted to turn the whole of a human body to gas you'd release similar amounts of energy to detonating the same mass of high explosives... which after all, are all about promptly turning a solid into a gas.
It gets even worse if you try and transmute them into energy (or rather, photons) by annihilating them with antimatter (or if you had the right sort of unobtanium, such as a load of suitable massive monopoles, catalysing baryon decay... the end result will be pretty similar, though the latter will release half as much energy because you don't need all that antimatter). About half the energy of annihilation is carried off as neutrinos which are effectively harmless and lost forever, but the rest of it... well, its about 5.7x1018 joules (about 1.3 gigatonnes of TNT equivalent).
Other things like throwing them into a black hole (or cloud of micro black holes) or stranglets would kinda more or less make them disappear, but that has other side effects like massive gamma release from the strangelets and the immense nuclear fire of evaporating black holes (or the issues associated with dropping a multi billion tonne black hole onto a planet, which may make the locals cross and reduce property values).
This leaves you with two bits of handwavium that might fit your needs. Maybe.
If it were possible to construct small wormholes, that would remain stable, and that were not so colossally massive as to be incredibly hazardous by themselves, maybe you could throw one at someone or something and have it removed. They'd still exist at the other end of the wormhole, of course, but they needn't be in the same shape as when they went in and the key requirement of having them vanish has been accomplished.
The second would be a way to efficiently convert energy or matter to neutrinos. Neutrinos barely interact with anything at all, and if you could annihilate someone and convert most of any resulting energy into neutrinos, they'd effectively vanish from existence in any practical sense.
I can't think of any means of facilitating the latter. It is almost entirely magic, as far as I'm concerned, but it isn't obviously impossible on the face of things. Just probably impossible, and almost certainly impractical if it were somehow possible.
Honestly, you could just shoot them with a normal gun. Why make life difficult for yourself?