I think there are some possibilities for a few heroic assassination missions, but I would have a hard time with a PC saying "I'm an assassin" and not having a paladin or cleric (or any self-respecting dwarf) ice them then and there....
One should never shine the light on one's own shady profession.
From my own gaming experience, to avoid being ganked by goody-2 shoes comrades, those who have played thieves and assassins who wanted that fact to remain concealed often had euphemisms for their PC's chosen profession.
"I'm a

...
legitimate businessman
honest merchant
information broker
marksman
trick-shot specialist
secret policeman
neighborhood tough guy
stand-up fellah
regular bloke
deft hand with a dagger
spyhunter
herald
traveling salesman
counterterrorist
specialist
warden
bounty hunter
government agent
the monarchy's left hand
and other such phrases.
This all reminds me of the brother of one of our old family friends. He got his bro an interview with his agency. The interviewer asked
"Have you ever killed anything?"
"Well, I've killed bugs and other vermin."
"Anything bigger?"
"Ummm...I did hit a deer once."
"Anything...slightly smaller than that?"
"No, I can't say that I have."
"Well, thank you very much, but I don't think you're what we're looking for at this time."
Now, I've personally never met the man. He's
always traveling...
As for Assassin adventures & PCs in particular, I've always thought that an Assassin is perfectly suited for a player who can't make all of the sessions. While his PC is away, you run his PC as a PBP adventurer. While the party takes the
obvious path to the sanctum sanctorum of the BBEG, the absent Assassin finds his own way...and then appears at the climactic final battle just in time to backstab him at a crucial moment!