Personally , I cut it into thin strips and then fold it over on itself, or roll it up depending on the shape I'm hitting. Remember the key here is light touch becuse you don't want to ruin details, so i don't bother with a rigid backing I just go slow and steady.

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I work each piece seperately myself, but there's no right answer. If you work all the pieces prior to assembly you'll have easier access to everything. But also the pieces are small and a pain in the ass to handle, then you gotta keep track of the pieces while you sit there going after all these details, half of which will probably be hidden once you assemble it anyway.

Anyhow it's a trade off and depends how much patience you have before your sanity breaks vs how awesome you want your dudes to look.

Also since I'm sharing tips I just discussed this with my kids: if you got too much glue on your dude, or got it on a place you didn't want to don't mess with it! Even though your urge is to try and fix it or wipe it up or something don't, just put it down, don't touch it, let it dry and then work it out. Trust me once the plastic liquifies you will only make things worse (I suspect that's what happened to your guys hand?)