Often you will want to search through your weapons for a particular type of damage - eg. "I'm about to fight enemies weak to X, what do I have that does that damage?"
Therefore, I suggest that when you use the 'Q' search to filter items, if your search term is an exact match for a damage type, the results should also include any weapons that use that damage type.
This does mean that eg. the results for "laser" will include both everything with laser in their name and anything with the laser damage type, but I think that that's probably a good thing and more useful than the current behavior.
Another, related possibility would be for it to include the skills that go into using a weapon (eg. searching for "throwing" would show all weapons that use throwing, while searching for "bravery" would show all weapons that use bravery.)