Those could be a little older than I suggested. Edges were not uncommon in the late 30s so skis without edges are probably older than mid 30s.
RUDOLF LETTNER AND THE STEEL EDGE
I have some older skis and they weren't varnished; they were oiled. Here are some photos of my 'best' wood skis.
The three pair that are dark appear to just be oiled. The lighter ones
may have a very thin layer of varnish. Note that the ones that
may be varnished aren't covered in thick glossy varnish like you'd see on a boat. You can click these images for a larger format.
The pair on the left in the first two photos are unmounted and have edges. The left pair in the last two pictures are 'used' and also have edges. The three dark pair have no edges. The very short skis were a friends when he was a kid and the ones with the leather strap and binding next to them were his mother's.
Others on the site may have more conclusive advise to offer.
https://www.skiinghistory.org/ (which provided the article on edges) is a wealth of information. However you restore the skis, I'm sure they will be beautiful. Be very careful with the leather.
Thanks for preserving skiing history. If you have interest in other pieces, you may want to look at my post:
Lots of classic and vintage skis I have some old leather boots to pass along too, if you are interested. I've kept a lot of stuff out of the land fill and it is time to let someone else care for it.
(And whatever you do, don't drill holes into the skis to mount them.
Somehow I don't think the thought even crossed your mind, though.
)