If you want to color the entire line and have a place to do it, you can use a Rit bath that is somewhat cooler than they recommend (in order to protect the properties of the line), say about the temperature of good hot bath water.
One I drove to Iowa to fish and forgot my gear bag and had to buy a cheap line and reel. So, I went to Wally World and got a 25 dollar Shakespeare combo, left the rod in the motel room and used the reel. At the same time, I also got a wallyworld Canadian made WF5F for 10 bucks, which was one of the best fly lines I've ever owned and for 10 dollars, by far the best value in a line I've ever seen. Anyway, it was white, which although i don't put much credence in line color spooking fish, i did not really want. So, I went out and bought a package of blue denim Rit, because I'd always wanted a blue line. I let it soak for a half hour in the hot (but not scalding) dye bath and stirred it now and then. Viola! Instant blue denim line that has not lost any color in 5 years of part time use. The only thing I'd do different if I did it again would be to stir the bath more, the color is a little blotchy here and there.
As an addendum, I haven't seen the Canadian lines in any of the walmarts in over 5 years. Pretty sure they discontinued it, as they do everything I find I like, from cars to chairs to shirts..