Somebody was looking for recs on where to buy wooden bendy dolls recently - it would definitely be more expensive but you could buy them and dress them up with fabric scraps or ribbons or whatnot... could be fun, but like I said, expensive.
I have a printed panel that you're supposed to cut out the Nativity figures, but I wouldn't do that with DS's help.
How about a felt board Nativity scene? My 2 (4.5 and 2) LOVE cutting out stuff with scissors, and the 2 yr doesn't cut neatly but we let her shred leftovers with safety scissors while my son and I cut on the lines.

Shapes could be either out of felt, or out of pieces you color and cut out of paper and then stick sandpaper or felt or velcro on the backs, or I've even heard of buying interfacing and tracing pictures onto it and coloring in with colored pencils and cutting out the shapes (did i hear that here? I dunno, haven't tried it yet, but I know I saw it somewhere!)