Usually guys are going the other way....a C20 to a C10 swap. To answer your question, yes you can install a C20 suspension, crossmember and all under your '63 C10. It will be the same as installing a '73-'87 C10 crossmember. You'll have to drill one hole on each side, and elongate one hole on each side.
Here's a thread that should answer any further questions you may have on the subject.
http://www.67-72chevytrucks.com/vboa...d.php?t=367260
If not just ask.