My kids want to compete in Judo and Wrestling. (And BJJ as well eventually.) I was trying to help them design their game around techniques you can for the most part do in all three. What Judo throws for example are legal in Folk Style Wrestling? Etc.
Hmmm. Honestly you're best off training wrestling moves for wrestling and judo moves for judo because even when they're the same basic throw, the lack of a gi changes the execution of the takedown. But to answer your question, you want judo throws where you don't risk giving up your back. So throws where you don't have to turn in. I expect Osoto and Ouichi will be the big ones.
I (used to) compete against Wrestlers who are also judokas, and I can definately see the benefits. I assume its similar situations of being in Gi and No Gi subs? Lots of overlays in techniques but some unique to its own styles? If you and the kids have the time to do it, go ahead..they'll have mad grip strength and a great sense of balance.