The tricky part with this scenario is that the missing player's character is key part of the next session. In that case the one-shot idea sounds good.
All of my players have multiple characters (one main + henchmen) - their adventuring company is sort of like a small mercenary band that is able to handle multiple jobs at a time. The henchmen have been sent on lesser jobs or, in the current situation, one a feint maneuver to draw attention away from where the mains will be mounting an incursion into enemy territory. That means we will be switching back and forth between parties and would make it easy to deal with a missing player.
A couple of other times when players couldn't make it and we were starting from camp or a town, I had the missing character go off on a personal job or, once, suffering from bad camp cooking and laid up with food poisoning. It also helps that we have six players so the party is still strong even with one absence.
In the past we have allowed a missing player to hand his character sheet to someone else but that rarely turns out well. If something bad happens, the proxy player gets blamed for mishandling the character. More than once the recap brought a response like, "my character would have used spell x or item y to escape that fate". I've also tried ghosting the character and bringing them in to do support. That is OK for a primary healer but the same "something bad happened while you were gone" problems arise.