Hi, both of those are good.
'Sipping at' a drink sounds a bit more descriptive, than just 'sipping' it, so is more likely to be found in a novel than in normal usage, but they both mean exactly the same thing.
I'm guessing the second part of your question is that you'd like to know how to re-word things to put 'sat' after 'sipping'.
If I''m right about that, it's doable but doesn't sound/read quite as good.
I sipped my coffee while sitting.
You could also use 'sipped at' instead of 'sipped'.
You could also use 'as I sat' instead of 'while sitting'.