Hmmm. Interesting question. Most airlines don’t accept cash anymore from what I can tell. Though it’s possible someone does. I travel pretty often and while I’ve not tried your scenario, my thoughts based on what I know of airlines:

On the gift cards, if you can do it with one or two gift cards versus many it may be easier. Some airlines (Southwest as example) limit the number of payment forms. Southwest only allows 3 forms of payment, so they may not accept more than 3 gift cards.

You may want to call whichever airline you are flying and ask something like “ I don’t have a credit/debit card, what are my options for purchasing a ticket”. They have almost certainly dealt with this before. If all else fails, you can also try going to the ticket counter at the airport versus phone/web. Sometimes easier in person when it’s out of the box.