The Charleton Background makes one of Assassin's main features, Infiltration Expert and Imposter, redundant. Yes, with the Assassin features, you can make more false identities, and with the level 13 ability you can make it so you don't need a check while the Actor Feat merely gives you advantage, but if you have Charleton and actor, you can make any class into the Assassin.
The only difference is Assassinate and Death Strike, for massive damage. But Assassinate will be used very rarely. And Death Strike, if you ever get there, is amazing, but again, the creature has to be surprised, and the DC is keyed off your Dex modifier, which in this case is extremely low.
So, with your build, you will likely not get to use Assassinate, as you are not stealthy, and will not be going first due to low initiative. You seem to like the "pretend to be someone else, sneak up and kill someone", so if you went Charleton and Actor, you can do that pretty easy. If you took a magic class with access to Disguise Self, like Warlock, you could do this all day long, having the Charleton False Identity as one of the faces you can conjure. With Actor, you can pretend to be anyone and look like them too. I've done that combo. Went through the entire Redguard base in Lost Mines of Phandelvor with a Warlock with Mask of Many Faces, pretending to be Glasstaff, led my party all the way to Glasstaff, killed Glasstaff and scorched his body, then told "my" men that someone had snuck into "My" office, and we've been found out so we all have to leave town. Defeated the entire dungeon with only one kill. Then I took Glasstaff's staff and started calling myself Glasstaff. Cause my last name is Glass.
If you don't want warlock, or hate magic, then just go Fighter with the Actor Feat and Charleton background. That gives you all kinds of nifty fighting toys to play with, and you won't be beholden to a rapier. Just shove an ax down their throat. You won't get massive damage to one attack per round, but you'll get multiple attacks and lots of options. Go with Champion for the increased Crit threshold, and crit 10% of the time for your massive damage.