Depending on how thin your accent strips are, you can mask them with automotive stripe tape. They sell thin tape for accents in any automotive store. They vary from 1/16 or so on up. Then just use a not-too-wet foam brush and I think it will be easier than you thought.

I did some dye work and I just masked it with masking tape that I stretched out and cut thinner with a straight edge and xacto. I air brushed my dye. I wanted to get a gradient from very dark on the bow to just the cedar color a few feet back. Looked great at first but the darkness hardly shows now. But just regular masking tape worked fine to keep the accent strips clean. You might be over-thinking a simple thing.

Just don't leave masking tape on too long. It can leave residue. Maybe the frog tape or one of those new types is better??
If your strip is thin you could give the auto stripe tape a try.