The problem with the "Safety Wire" pliers is that they do "twist" the wire, rather than just wrapping the free end around the "standing end" like you want. The twist in the tensioned side of the string will weaken it significantly when you try to tune up.
This may be okay, depending on the instrument you're using the string on, but if it's going to "speak" well, the string needs to be pulled up to fairly close to its breaking (yield point) tension.
Form a loop over something round that's close to the size you want for the final loop - I've used the smooth end of a 5/16 drill. Wrap the short end around the main wire. Try to keep the first few turns at least so that they touch each other. Put on quite a few (10 or more) wraps. It helps to keep enough tension on the "main" side to keep it fairly straight.
Trim the end, and then use a round and smooth pin of some sort to pull the loop out "long" like you want it. If possible, do the final forming over something that's about the same diameter as whatever it will hook onto on the instrument.
Commercial string mfrs use quite a bit of tension on the "wrap" side of the wire, so that it bites into the main wire. Since you can't easily do that - without weakening the wire - just add a few more turns.