Dear Mary,
As you probably know, red gold becomes more yellow when heated and pickled. Coupled as mentioned below with a good close join, you can easily get away with yellow. You could also get your customer on side by explaining this at the start.

Now the point is that 10mm of 0.5mm medium wire solder from Cookson would snip into pieces and be enough for your ring. The cost would be around £2.00 including postage. Regards, Dennis.

https://www.cooksongold.com/Solders/...-HPB-720&add=n