In a lot of examples, commutivity is obvious:

> - The two computers can easily swap data.
> - We swapped houses during the children's school vacation.
> - Do you want to swap places?
> - If you prefer to sit next to Chris, I'll swap seats with you.
> - When you've finished reading your book, and I've finished mine, can we swap?
> - We swapped addresses with the people we met on vacation.
> - We spent the evening swapping (= telling each other) stories/jokes.

But the non-commutative sense may be the default as in this specifying definition (in the examples given, it is contextually forced)

> **swap someting for something**: to exchange something you have [or in hypothetical situations would see yourselves having] for something else:
> - Most consumers said they wouldn't swap the product [they owned / desired]  for a cheaper own-label brand.
> - They've swapped their old car for a much larger one.
> - When he got a job in a bank, he had to swap his jeans and T-shirt for a suit (= he had to wear formal clothes instead of informal ones).
> - [ + two objects ] I'll swap you my chocolate bar for your peanuts.

(All quotes so far from [Cambridge Dictionary](https://dictionary.cambridge.org/us/dictionary/english/swap), re-ordered.)

But as I expected, counterexamples aren't hard to find on the internet:

> - "I'll swap you your pasta salad, for this apple", my friend would tell me.
> - I'll swap your flat mate for mine ..."

ie 'I'll / I would exchange something else for something I have.'

So 'I'll swap A for B' does not entail that it is A or B that you have. You have (perhaps hypothetically) one of them. Directionality (who is the donor and who the recipient) must be indicated by context, though A is more usually owned by the speaker.