The goal is to ONLY have the part of the line you are handling or cleating to have the cover on it. This helps with the line running through the blocks and decreases weight (ya gotta be good to make that weight difference count!!!)
My suggestion is to take the cover off on a small section first then if you need to you can take more off. A little more work but you do not want to try to pull on the core of the line to snuff the spin. You may get away with last couple feet being the core, but nothing more than that when snuffing. I use 1/4 (rather large compared to what a lot of people use I think) warpspeed that has a dyneema (aka spectra) core. I actually over did one end so I switched around and tapered the other end! So the halyard side is tapered which doesn't create a problem because it isn't nearly the 25 or so feet long to create a prob raising the spin AND the snuffer end is tapered also to about the right length. I coudl probably take off another couple feet but I haven't noticed a problem at all. You can taper almost any line that is double braided but you need to make sure the core is braided (some older 3/16 line has parallel core which wouldn't work to taper for obvious reasons). 3/16 crystaline might work well but that line has a lot of problems with "hockling" I guess would be the term- where it bunches up sometimes where it goes aorund blocks or through cleats.