Actually the set in the teeth is less pronounced the finer the teeth, and at need you could get by with a single crosscut saw with fairly fine teeth, not ideal but certainly workable.
When I bought the two tenon saws mentioned above I was to say the least rather inexperienced, and I tried them both with little regard to crosscut or rip. Naturally the rip saw disappointed and I set it on the rack always there but uncalled for. Flash ahead a few years and I was trying to saw some white oak tenons with my brass backed crosscut, very slow indeed.
Out of frustration I picked up the other one the one with the steel back, and tried it. Surprise surprise not only did it suddenly seem to be capable it worked exceedingly well. Have a look around at antique stores, second hand stores and such, they are out there, and the hunt is rather fun to. Generally they won't break the bank.
Oh you asked I believe about using the heavier tenon saw for dovetailing, no problem if you get used to it, it will work just may be somewhat unwieldily for such a short cut.