There are a few issues with welding thin aluminum.
I have welding experience in MIG, TIG, oxygen acetylene. Welding mild steel, aluminum, stainless steel of various thickness, 22ga or less and 1" plus. I have learned while working on making cars go fast, welded at CAT road paving devision for a while and a few other places.
If the parts to be welded are used, dirty, anodized, painted, un known aluminum alloy, acheiving a good weldment that will withstand the stress and pressure of being a hobby or high power experimental motor could be difficult and without previous working experience and testing could be un safe.
Welding process: braze, TIG, MIG spool gun. I have not braze welded aluminum but other metals, a spool gun will burn to hot for this kind of weld.
TIG, not just any TIG, but one with pure Argon shielding gas, 1/16" pure (green) tungsten, the ability to weld in AC, high frequency and ball the end of the tungsten.
What thickness is the fin? The case at .059" is thin, I have welded car radiators, the tubes in the core of the radiator are thin, it's not fun but doable.
The other issue I see is only having the back edge of the fin welded could cause instability and the epoxy or what ever glues the front part of the fin may snap off, or degrade with the heat of the burning motor.
The biggest issue I see is distorting the aluminum, if welded properly the reduction of the temper of the aluminum from welding could be offset by original material thickness and the additional filler rod creating the weld joint, if its 6061 T6 aluminum I would select either 4043 or 5356 alloy 1/16" filler rod. The 4043 will be easier, cleaner to weld, but be softer overall. The 5356 is a structural welding rod and will have a different look but be a lot stronger. The internal bore will distort during welding, the more welding rod you add the more will migrate to the ID of the tube, the oxidation layer on aluminum melts at 3700° F, where as the aluminum itself melts at 1221° F. There are many ways to remove this oxide layer and is critical to the welding process.
When I try this later this year I will have a elaborate fin jig to hold the fins during the welding process, I will be over sizing the tube I am welding the fins onto, then boring the ID to what I need to attach to the airframe or slide over a motor case, I do not plan to weld onto the motor case directly.
~John