Don't think you can avoid assigning them to the militia since it's the only way to get them to wear items with [ARMOR LEVEL x] tags. (Which is the tag that appears to exempt clothing items from wear.)
You can mod RAWS to add the tag to various clothing types and then get cloth "armor" that won't wear. However, your civilians (and arriving migrants) will not be wearing anything of that type. Therefore, do not mod all types for an particular area; e.g. trousers and skirts.*
For example: You could add [ARMOR LEVEL: 1] tags to tunics, trousers, and mittens. Then make sufficient numbers of these (and something like leather boots - which are already armor items) to equip squads of civilians. And set up a uniform set to replace clothing and using these items (plus a cloak, hood, crossbow, etc.). Once you have enough to equip the squad, make one a militia captain in the nobles screen and then the desired civilians to the squad. Between jobs they should gather a set of equipment and then will be fairly happy with their no-rot clothing. Plus now they walk around with a crossbow and quiver of bolts and can act as a sort of secondary defense for the fortress since they will pot-shot at intruders sometimes before running away.
Per militia assignments you can do relatively low impact by creating squads that stay inactive, have no training schedule (all months set to no training), and I guess you could skip giving them a barracks. I do assign them a barracks, a crossbow, bolts, and then skip giving them an archery range to waste bolts at. And then they go do individual combat drills when idle rather than looking for, or starting, a party.
One thing to watch for though is assigning woodcutters, hunters or miners to squads while that task is active. They have a hidden "default uniform" that will conflict with your assigned one. Which is a pity since those are outdoor roles that would greatly benefit from potentially having heavier clothing to wear.
* - Been there, done that. Had the tantrums.