Uhhh...you could have some problems there!
A mig/tig system often has a RF component to initiate the arc, and that could make the device go haywire.
A buz box, especially one running in DC mode, might be less likely to generate interference since it is mostly low frequency noise.
In either case, a really good earth ground, grounding of metal work surfaces, etc, might help a lot. Keep the welding leads draped as far from your body as you can...keep the welding unit as far away as you can. Magnetic fields fall off rapidly with distance.
Of course, any sort of induction heater would be right out!
Emi filter on the mains might be wise:
https://www.edaboard.com/threads/198697/
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I know that some broadcast engineers wear Radiofrequency Protective clothing when working near hot antennas, such as this:
https://www.osha.gov/pls/oshaweb/owadisp.show_document?p_table=INTERPRETATIONS&p_id=21095
https://www.lessemf.com/personal.html
https://www.norad4u.com/emr-protection/rf-protection#TOC-RF-protection-clothes
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also, look starting on page 34:
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And of course, if you are wearing a metal RFI shirt....you have to be really careful to no electrocute yourself!!!! NO touching bare electrodes, etc. Wear rubber soled boots. Try very hard to not use both hands....you do not want to be holding electrode in one hand and resting other hand on workpiece or grounded equipment/table.