Hey Brandon,
As a retired Master Gunsmith, I would strongly suggest to simply use the O/A-fuel you have. You cannot control the TIG arc as well as you can with an O/A flame. The flux would probably burn off too quickly with a TIG arc & the flux is what allows the sil-sol to flow nicely via the capillary action. Having done close to a hundred double barrel repairs way back then, nothing was as easy to use as O/A. Your main concern is to have the barrels clamped in a way that other areas of the ribbing & barrel bottom joint panel doesn't also loosen. Some can be a nightmare & I had on several occasions turned down repairs because of someone else, completely inexperienced, attempt to do a repair such as you describe. They completely destroyed the integrity of the barrels & ribs & firearm was scrap. I would also suggest you find an old dbl bbl & do some practice as I did when I first started. I never took on a job that I had not done before with many hours of practice to develop an extremely confident repair. You can try the TIG...... you will see for yourself. Mistakes are learning tools.......just don't let it be on a customers' pride & joy....

Denny

I know guys who do a fair bit of TIG brazing, but before suggesting that You can or can not do the repair You mentioned, I think You have to know the melting point of the solder used originally, and be sure what You plan to use melts at the same or a little lower.

The term "silver solder" covers a lot of products.