From Merriam Webster:
Main Entry: 1swap
Pronunciation: 'swäp
Function: verb

transitive senses
1 : to give in trade : BARTER b : EXCHANGE 2

intransitive senses : to make an exchange
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So I guess one can give money in trade or exchange, but many would say
swapping is cashless. Maybe from our childhood -- I'll swap ya three green
marbles for that black one. A Superman for a Batman (comics)

Then there is Husband Swapping (sic)

I certainly don't swap for my groceries -- I buy by paying cash,
credit, or food stamps (just kiddin on the food stamps)