I did a similar one for Deans to EC3 ( both ways ) and didn't even use any wire... just direct soldered them together and then added some shrink wrap around the two connectors. Just make sure to get the polarity correct and you're golden.
Check your ESC's specs and see if it can handle a 6s. If it cannot, then don't hook it up. If it is made for 6s, then the BEC will likely work just fine. If it's not, then it will likely burn up the entire ESC, not just the BEC.