In my experience, I tried the exact thing as you want to attempt. I was told by my LFS
that if you add them both at the same time, it would be better. I had my yellow in there for about 1 month before adding a slightly smaller regal tang. The yellow kept chasing out of the rock caves, hideouts, etc. It would use it's tail and keep whacking it. I don't think it did any major damage to the regal other than stressing it out, and it did eventually have to find it's own home... then about 1 -2 weeks later, they were getting along. Tangs are pretty sensitive, especially the regal one. I've had problems with just the regal developing what I think is ICH in which my attempts to help it probably led
to it's demise.
With my second experience in adding tangs, I did get to add both at the same time, the yellow smaller than the regal, and they didn't fight at all.
I've been advised many times that a bigger tank is recommended for tangs though, especially after they grow a little. Good luck.