I'll take a quick stab at an answer. First, I'm not going to say that you unequivocally can't skate ski outside of a groomed trail. If I did, someone would probably quickly follow up with examples to prove me wrong. And when conditions are right and a good crust forms (in the spring in my neck of the woods), you decidedly can skate ski just about anywhere. That said, conditions are not usually right for crust, and skate skiing in ungroomed snow is very, very difficult. Are there packed snow machine trails or anything in your area? Trails that have been packed by fat bikes? I've taken my skate skis out on pretty narrow trails where the skis are not necessarily at their best, but I've been able to cobble together a ski. In untracked snow, trying to skate ski becomes a real chore.
I wouldn't write off classic skiing as not beneficial to cycling. Its hugely aerobic. It still hits the leg muscles, the glutes, the lower back. I mostly skate ski, but when I do pull out the classic skis I definitely feel it in different muscles. Both skate and classic really rely on a strong core. While no expert (and nowhere near an elite cyclist myself), I would think you'd get cross-training benefits from either or both of skate and classic skiing.
If your interest is in skating, I wouldn't get classic skis and try to skate them. The cambers are very different. Different tools for different purposes. And to my knowledge, no one makes a skate ski suited to ungroomed snow. A lot of manufactures make light touring skis, usually waxless, designed for skiing in untracked snow. I'm going to guess if you don't have access to groomed trails you also don't have access to a shop that specializes in xc skis? That would limit my advice on your questions as to what to look for in skate skis, as I would say to look for a shop that will take the time to properly fit you to a ski with the right flex and length for your weight.