I have welded (stick, mig, tig) on several modern cars with solid state computers with no issues. The key is good quality grounds in locations that keep the electrical flow contained within the steel parts you are welding. That electricity won't want to flow out of the frame through the aircraft ground into avionics and back out of avionics (if electricicty goes into avionics via ground, it must come back out on the positiive side and find another patch back to frame ground) and back to the frame unless it can't get there more easily through the frame itself.
If the current put in via the electrode can't easily get back to the ground cable (which really isn't a ground with TIG - DCEN), You can expect it will start flowing other places that might get it back to the machine. For example, start all tack welds on the side of the frame that has the ground cable attached. After the first tack weld, all is good. This will mean taking off paint in another area of the frame in some cases.
I am no expert, so don;t consider this advice, just someones experience.
Larry