I have heard "skal vi sjå" so many times I didn't even realise it was not an accepted bokmål form
Yes, it seems so common that people don't normally react to it, whereas if someone who normally spoke Bokmål said "Eg veit ikkje" in the middle of a conversation, people might smile.
"Sjå" is only used in this set phrase - a person from SE Norway who says "Skal vi sjå" would not say e.g. "Jeg skal bare ut og sjå på rosene mine". As you say, words get imported from other languages, but usually they're then used in all kinds of contexts, not just one phrase.
Comparing with English again, you might find some speakers from England who say "I dinna ken" (Scottish for "I don't know"), just for fun, or as Ben Jamin says, to add some colour. But like "Skal vi sjå", it's only the one set phrase - that person wouldn't say: "It's difficult to ken what to do".
Just now I remember one such example: Vi tar det från början.
Then there's "...eller hur?" which maybe fills a gap in Norwegian because people don't say "...eller hvordan?", although of course there are other ways in Norwegian to express something similar: "(eller) hva synes du?", "ikke sant?", etc.