It's really surprising that DC Comics never paired these two up in an adventure. Considering they both are schooled in the same areas of discipline, have a similar modus operandi, and each did a fair share of time traveling... it should've been no problem. After all, what's a few hundred centuries for fictional features like these, one born in the 1940's and the other in the 30th Century.
At least Karate Kid journey back to the 1970's for a brief period, and when last we saw Judomaster he had been shunted into 1986. Course, the Kid perished soon after returning to his native century, however an earlier incarnation may've been drawn into the past using a Legion time bubble to check out the original black belt whitey?