Don't hang them. Use an upright holder that you can move and stash away.

Not my picture...but good idea :)

I have a rack that hangs on the inside of the cabinet. No screws and the hanger is padded so it doesn't rub. Spectrum 76771 over the drawer/cabinet paper towel holder. I also have the other kind that stand up on the counter but I like having less out on counters.

I rarely use paper towels; too wasteful. But there are some gross things I'd rather use paper on and just toss. I keep my paper towels in a drawer. When they're out on the counter, others in my family grab them all the time. But not so much from the drawer.

sometimes a paper towel is the lesser of evils. I keep a basket under the sink of cheap washcloths for wiping down in general. I keep a dishtowel hooked through the handle on the trash pull out so I can grab that instead of messing up the handle.

Live with your new kitchen for a few days and see what you need/want. Somewhere in between is your answer.