When I started using the stranded cable for leadouts, I went with a method used by one of my flying buddies.
The leadout cable is slipped into a section of annealed brass tubing. Usually, the 1/16 OD tubing is used but you can find some metric sizes on line as well. Enough cable is pulled thru to wrap the leadouts as Dan suggested. The brass tube is then bent into a teardrop shape, using something like a 3/16 or 1/4 drill bit to bend it around.
The eyelet, or thimble, can work as well, but I like the brass tube method.
Yes, avoid the crimp. Another method is swaging. There are tools and components to do swaging properly. I have done that before. No failures, it seems to work OK, but I used it on smaller planes only. The fear I have with the swaging is that you are left with a very stiff section, right at the end of the swaging sleeve, and then the "unsupported" cable, which is prone to flexing right at that point. This could lead to early failure.
Wrapping, although tedious to some of us, works very well, even if not a perfect wrap. It avoids that stiff-flexible problem of swaging, and I can't remember seeing a line wrap, or leadout wrap, fail.
I proof load all my leadouts and lines before putting them in service. You never know what might happen, and I feel better knowing I subjected the components to the required pull test value.
And, solder is not needed anywhere in the wrap.