I'm confused here. You're mooring against a dock?
Are you docking alongside a dock? Or moored to a ball? Or docking bow/stern in, med style?
I've never heard of thimbles being used or needed in a docking line, which is normally cleated off in the US. (I'm probably losing something in the translation, I'm not really fluent in Canadian. (G) )
The purpose of 3-strand docking lines is that they have some natural spring in them, as you pull tight they untwist a bit, acting as a torsion spring for their entire length. A braided line can't and won't do that, making it unsuitable for docking or mooring lines as it will chafe instead of stretching. Sure, they feel smoother and can be used--but they're the wrong line for the job. Wornout halyards, etc. are often the source of braided "docking" lines, just being used a bit longer before they get scrapped.