Resistance wire apparently is a key component in vaping pipes, or whatever one vapes with. Which means you can now cheaply buy a vast assortment of sizes and types on Amazon--I haven't checked the ubiquitous strip-mall vape shops to see if they have it, but others might be more adventurous.
Important b/c so many areas of the sender are under rivets or simply inaccessible that, even if you clean all accessible contact points, the resistance likely varies from one sender to another, regardless of the wire. Likely need somewhere between 36-42ga depending on material & the status of your sender. I would also be cautious with the suggestion that removing the solder requires more heat than you'd anticipate. It's true, but the terminal ends are too delicate & don't hold up well to direct heat and you don't want too much heat transferring to bind the swivel terminal base. My terminal tip is now about 1/4 the size it was (stop it, I can't think of another way to say it), because it didn't hold up to heat trying to remove the old solder. Dremel & patience. If you don't have jeweler or small tools, go buy a beading tool kit from hobby store--about $10-$15 with tiny tweezers, snips, pliers, cutter, etc.