"Check with your airlines" is a good suggestion, but lets go to the basics first.
Nothing that I've read about the SBH testing requirements mentions anything more specific than rtPCR. Is the saliva test which you mention rtPCR? If not, it's a non-starter. Antigen tests are no longer accepted.
Not all rtPCR tests require the long swab which many detest. I've had two tests, both of which were done with Anterior Nasal swabs which went no more than an inch or so into my nostril. Easy, no fuss, no pain, over quickly.
Depending on the route which you are traveling, you may have another consideration. If you're traveling through SXM then you have to comply with the SXM EHAS requirement, even if you are only in transit.
https://stmaartenehas.com/travel-requirements/ Same for your return trip.
Returning to the US, the CDC website does not specify the type of test, only that one be performed within 3 days of arrival. An Antigen test at the Red Cross testing site, or at one of the island Pharmacies, would be accepted.
https://www.cdc.gov/coronavirus/2019-ncov/travelers/international-travel-during-covid19.html