I just picked up a muffler which has had a K75 exhaust adapter welded onto it.  I know the muffler is stainless and I believe that the adapter is also stainless.  I'd like to dress the welds flush to the metal surface and polish the metal if possible, but I'm unsure whether doing so will compromise the structure causing a premature failure.   Can anyone advise me based on the picture of the welds below?

Anything that is structural you never dress the welds. Seeing as that isn't structural then you are fairly safe to dress them but (as always a but) looking at the welds there you will need to do some more welding before the dressing as there a lot of undercutting on the welds that will need to be filled. If you don't fix the undercutting and dress it back to a smooth finish too much of the parent metal is removed making it thin and weak.

Thanks Rick.  I guess I'll be lazy and forego dressing the welds then.  I don't have access to welding equipment nor do I have welding experience. So, I'd be dependant on someone to fix this for me (probably big bucks).  It's in an innocuous part of the exhaust line so the welds don't matter too much; I just thought it would be nicer looking all ground smooth.

You could tidy it a bit, as long as you avoid cutting into the parent metal at all.
A decent weld (this isn't one of those) should be at least as strong, if not stronger than the surrounding steel.

As Berko say's you could touch it up abit without touching the parent metal, and then take it to your local muffler place, they who do nothing but weld up exhaust systems would probably do a touch up on the daggier bits for bugger all dosh and you give them something alittle more entertaining than they are doing every day of the week, they do after all love a perfect weld job, especially if its out of the normal range of things to do.