That seems rather a broad question. What sort of job are you referring to? I'm no expert on tigging stainless but I'm sure with more info someone else can help.
It's a how long is this piece of string type of deal... 'stainless' covers a lot of ground beyond plain 'ol 304L and 316L, no filler wire on an outside corner is a very different beast to an autogenous fillet weld and then there's service environment; corrosive environment versus garden furniture vs something that sees 'kin hot temps or temp cycling etc etc
Wire all the time is 'safe', no filler needed as an absolute statement is just plain wrong. There are plenty of times when autogenous is more than good enough, common sense covers a lot of them for example even with a perfect fit up most people ain't gonna be able nail a butt without undercutting (notches make great stress risers) unless they have some posh orbital welding kit and know how to use it. If it's say a shopping trolley dock/park thing undercutting and/or partial pen welds aren't a big deal but blending the weld out and regraining for cosmetics would be so you need to use wire
The common one is the outside corner and set correctly can be as sound as a filled joint. (One side slightly protruding so it can be melted and used as reinforcement).
Butt joints and inside corners where your joint is determined by the face sides on your material are more suitable filled as a properly reinforced joint is far stronger under stress. That said as a Micky mouse splodge seems to the trend on a lot of "welded" stuff we see and buy today so an under cut autogenous run will be fine in some cases.