I think you should.

I've only had Vita have one area shaved, and only once; the area that needed it.

Make sure the groomer is licensed to do cats.

That one time, I took Vita in to a PetsSmart, and was very pleased. I went in and spoke with them first. Got an early appt., they took her while the others were checking in dogs, so everyone was free to help if needed. I stood and watched through the glass. In and out in 5 minutes.

Does it really matter if she gets embarrassed? I mean, this is not healthy for her, and when mats get tight enough, they can pull the skin and hurt.