The other question I suppose is which of the seven do you want to finish on?
Cabot should be doable without using your arms, although if you go over the Bulge & near The Horn, it's got a couple of decent climbs, should be arms free but it's far from flat.
Garfield's top might have a couple of spots where one hand might be good for balance. I have to go reaqauint myself, It's been a few years since my last visit. It's also one of the best views you have left. The ledge near North Twin are good for views, Moriah & Isolation being real good too. (Zealcliff good, a fair distance from Zealand's summit)
There are a couple of ladders on the way to Zealand, an experienced hiker probably could get up them using just one arm. The top of Isolation provides the only view & it's a beauty, wouldn't want to tease your friend with your oohs and ahhs.
Owl's Head is flat until the slide, might be able to get to the base of the slide where a view could be had while waiting for you to summit. (Disclosure, I'm not an OH fan)
Moriah from Bangor Road might be possible, it's a fairly steep ramp up (some PUDs) but I don't recall serious arm work. Going up from Route 16, there is a climb right near the top.
I'd do Cabot as it's maybe the easiest & least appealing of the remaining ones left for views. (has a couple of spots though, don't they all - except South Carter....)