Base what weight spey rod you get by what distance you need to toss the flies. I look at two handers not by what you want to catch, but by how far you need to deliver a fly. You can land what you want to on any two hander. You may not be able to cast as far as you want however, with any two hander. You need to look at this as a delivery system for the fly, not a fish retrieval tool.
If I remember right, you said up to 120'. That means a fairly big rod. I can repeatedly hit 140', and by repeatedly, I mean pretty much every cast, with a 15' 10/11 wt. rod. I have hit maybe a tad over 150' trying to pull Mooneye that were surface feeding behind the first railroad bridge piling. By the way, those cast were with big clousers. If I mess up any part of my form on those casts they don't go that far.
I'm pretty sure you can hit 120' once you get the kinks out of your cast with a 14' 8 wt. or so. 14' 7 or 8 would be what I suggest. That and wear your fur chunks fur to the inside. It tickles when you walk and is just more fun.
Again, you don't want to use a skagit. You can but I don't think it's the best tool for the job. You can use a scandi if you want. I see no problems there other than I just don't see hitting really long casts underhanding it.
Now I think one of the things that make people think the skagit lines may be what you want to use is the line "for big flies". But they may be thinking about what big is in a single hand trout type thing. Seriously, I toss stuff big enough to make a huge bass think twice about messing with it in case it can fight back.