I don't know how involved you want to get but it sounds like TIG (tungsen inert gas) welding is what you want to do. A good welding/fabricating shop would have a TIG welder. TIG is great on a variety of thin metals including stainless steel. This is the type of welding used to fabricate exhaust systems used on race cars and on many full scale aircraft parts. But, it requires a relativly expensive machine and a very skilled welder.

Soldering with low temp silver solder is different from silver soldering. The low temp stuff, like from Great Planes, has a low silver content and using soldering iron temps. As the metal is heated and the pores expand, solder flows into the pores to great a bond. All the low temp solders do not allow for enough expansion to be as strong as brazing. And, the solder itself does not have much tensile strength. In other words, a lap joint would be much stronger than an edge joint. Or a joint like copper pipe in an elbow would be very strong because the pipe fits inside and the solder flows in by means of capillary action.

Real silver soldering (not to be confused with the low temp mentioned previously) is similar to brazing in that it used much higher temps than regular soldering. The metal is heated to a cherry red color for brazing and to just under that for silver soldering. Because silver solder is thinner (less viscous) when melted, it flows into joints and pores at a lower temp than the brass alloy rod used for brazing. But the silver solder is the strongest of these types of processes when a lap joint or similar joint is used. When brazing with brass alloy brazing rod, the metal can lose it's temper because the temp reached is in the 1500 degree F range. Silver soldering reaches approx 1100-1200 degrees F.

TIG welding, if done properly, is great for lap joints, T joints, etc. You can use a very fine tungsten electrode and fine welding rod to join very thin metals. The metal can then be heated and quenched to restore the original hardness (depends on the metal and the exact properties it had before). Small parts can probably be done at home. Or a tool room (business that make tools and dies) can likely help with that.

If you have any questions, let me know. I used to be a welder and a tool and die maker.

Good luck,
Jim