Having done them all at least twice I'd be okay doing a peak withgood views knowing that I would not see one.
Brook Crossings & how wet the trail is + wind are issues too
Madison Via Valley Way if wind was under 30 would be okay, waste of a peak with great views
North Twin would be my first choice if crossings were not high (a rainy day after a long dry spell) I think they will be high or at least above normal
Cabot okay although will all the rain I think a lot of these trails (except the closed one which may be more brook like) will be wet & muddy with ponds of water in places, especially around Unknown Pond on the Kilkenny
South & Middle Carter a good choice, parts of Carter Dome Trail between 19 Mile & the switchback will be very wet, very muddy, other than that just enough exposure on Middle so in bad weather, you get a taste of it & then back into cover
Owls Head same as North Twin for issues
Tripyramids I'd skip North Slide & do loop with Scaur Ridge & down South Slide, at least one crossing might be interested but IMO (from memory) not as bad as those on N. Twin Trail.
Wildcats okay, expect a fair amount of standing water in places & I'd go up E because I'd rather go up the ledges more likely to be slick than down them. (I prefer doing Wildcat the other way though)
Moriah has great views, would be okay from Stony Brook but lots of ledges & views would be wasted
The big Three Presidentials just have too much exposure or steep trails that when wet would be unpleasant to descend, that said if wind not an issue, Adams via Valley Way (hut for shelter) or Washington via Jewell would be doable, very exposed for a real long time (read borders on stupid) but trail is a good one in slick weather. Ammo trail when real wet IMO should be avoided unless you have a decent amount of experience on it, if the wind was not bad, I'd go up it & down Edmands but that is a long time to be up there in bad weather.
Of which I've had my share of BTW...