Putting pin(s) back into chain
It's safer and way easier just to buy another MissingLink (KMC's name for their master link design) of the same type (pin length) the chain came with, leaving you with an inner link that has one on either end. They're around $2US.

In addition to saving the trouble of getting the pin back in there, there's also the question of the integrity of modern outer chain links once they've had a pin pushed back through, even in the more normal circumstance of pushing a link halfway out for chain removal. Every current major manufacturer of derailer chains except KMC says not to do this, due to the risk of the fit not being as tight after re-insertion as it's supposed to be. I've long wondered whether there's actually anything different about KMC in this regard, but I know that modern chains in general are prone to breaking, usually during hard or fumbled front shifts, when they've been reconnected the "traditional" way. I wouldn't venture to guess what the odds are of it happening, probably quite low, but putting in another MissingLink eliminates the risk. They're very trouble-free. Having a couple close together may seem goofy but doesn't cause any issues in practice.