I need to MIG weld some 3mm stainless to some 4mm mild steel - nothing structural but it needs to be a reasonably good weld.
Which wire should I use - mild or stainless?

Mild steel will work, but do not expect the weld to be strong. Another option is silver solder. It all depends on the abuse it will get.
Or, get someone to tig it for you using a 'dissimilar' rod.

As long as its not structural normal mig wire and loads a power will give a nice weld.

we discussed this last week and
our coded welder @ work says to use
stainless but for best results you need
disimaler , i think this applies to stick

I welded a steel exhaust to a stainless silencer adapter using ordinary steel MIG wire, worked OK for me

I made a pair of stainless inner wings for my Discovery and welded one side with SS and the other with MS (I ran out of SS!). There was no noticable difference. I s'pose the chromy stuff all gets mixed up anyway!!

just remember the vapours

I think I'm turning Japanese? They were definitely one hit wonders Are they welders now?