It got into my brain long ago, from the PNW.

Like "Oooof." Or "My goodness."

So I guess it's in my brain to be used in its gentler sense.

"North American usage 

Uff da is a general purpose expression of surprise, astonishment, exhaustion, relief and sometimes dismay. It can therefore be a substitute for common obscenities. [9]" 

"Uff da - Wikipedia" https://en.wikipedia.org/wiki/Uff_da