Setup
In my campaign, one of the PCs is an assassin.
Before the game started, I gave the player a list of assassination targets. One of the targets happens to be friends with the party's warlord. It's been interesting, as there have been a few points where the assassin could have killed his target, but not without alerting the warlord.
Problem
The player would like his character to sneak off alone in the night during an extended rest, or at some other point when the part is split for a while, assassinate the target, and come back without anyone being the wiser.
This seems like a good plan to me, but I had a conversation with the player, and we're both concerned that roleplaying this event would result in me and him playing the game while everybody else sits and watches.
Possible Solutions
I've considered framing this whole event as a skill challenge so I can just have the player roll a few dice, find out what happened, and get back to the action. We don't really like skill challenges though, so I'm a little hesitant to throw one in just for this.
I've considered finding something for the rest of the part to do in the meantime, like giving them a puzzle to solve they have to talk about, or putting them in a fight with an enemy I don't have to think about much, something like that. This might just end up being chaotic and poor for everyone, though.
I've considered having a session with just me and this one player to determine what happens, and then informing the rest of the group when we play our normal session. This is not super-convenient, but may be the most fair to everyone. One serious problem with this approach is the in-game timing of the event. We're halfway through a session, the party decides to take an extended rest, the assassin wants to go assassinate... and I tell him what? "We'll do that this weekend. Just assume you didn't die and came back so we can continue this session"?
Question
Have you ever done something like this in one of your games? How did you handle it? Did your approach work? What works best?
We're playing 4th edition Dungeons and Dragons, so keep that in mind if you have a system-specific answer, but as this is mostly a question about managing the table I'd be happy to hear answers citing applicable experience from any edition or even other games.
Note on the Nature of the Assassination
I don't want to make this question so specific that it only applies to my situation, but I was asked for more information on the nature of the assassination in this particular instance.
The assassin is a monk serving the god of death. The assassination target was given to him by his monastery, and originated as an order from the god. This is one target on a list, and killing the targets on the list is the character's primary goal.
This particular target is not dangerous, just a harbormaster, but others on the list are extremely dangerous.