I could see Vegeta being able to do it being a Saiyan and being able to pick up Ki related techniques easily. Piccolo probably could have. He was a direct rival to Goku when Goku arrived on Kaio's planet and was basically his equal. I don't think his healing would influence his usage of Kaioken given that it merely regenerates limbs.
I highly doubt Tenshinhan could learn it given he was on Kaio's planet for so long and never used the technique. It's possible he learned how to infuse it into his Kikoho to create the Shin Kikoho - which was powerful enough to hold down Semi Perfect Cell. That's not possible without an outrageous amplification.