Two options, both airports are 1-1.5 hour drive to the Falmouth/Mashpee area of Cape Cod:

Logan Airport in Boston, MA: If you are planning to extend your stay and sight-see in Boston (or Salem--it will be close to Halloween!), then Logan Airport is best.

TF Green in Providence, RI: If you are planning a quick trip in and out for the Wedding, TF Green is easier.

TF Green Airport is a smaller airport, with car rentals within walking distance, and less traffic/congestion. Logan Airport can be congested with Boston traffic and construction so plan extra time. Please note that you must take a Shuttle to get to the Car Rental Center.

Car rental options at TF Green include: Alamo, AVIS, Budget, dollar, enterprise, Hertz, National and Payless.

Some airport shuttles to consider:

https://elitecarserviceandairport.com/

https://gogreenshuttle.com/

https://capedestinations.com/airport-shuttle-service-cape-cod-boston/

https://bostonairportshuttle.com/cape-cod-ma-shuttle-taxi-4

https://www.uber.com/global/en/r/airports/bos/?_csid=56lNPdiQWXBO91zzdM2xBg&ad_id=670078782610&adg_id=155667642390&campaign_id=20410433182&cre=670078782610&dev=c&dev_m=&effect=&fi_id=&gad_source=1&gclid=CjwKCAjwvvmzBhA2EiwAtHVrbxA0VPuEMWFbuTA1E6KIb4Kx4DrImZhtdGi6actWWXUUBhbfDyw4SxoC5hcQAvD_BwE&gclsrc=aw.ds&kw=airport%20shuttle%20pick%20up&kwid=kwd-297918879581&match=b&net=g&placement=&state=YRQdqTnhbxaUrZHXJTwEkI9odPfHbq4HM7s4yZ7NzoI%3D&tar=&utm_campaign=CM2335831-search-google-nonbrand_1_6_US-Boston_r_web_pme_cpc_en_T1_Airport_BM_reserve_airport%20shuttle%20pick%20up_kwd-297918879581_670078782610_155667642390_b_c&utm_source=AdWords_NonBrand

Peter Pan has buses that go directly from Logan Airport to Falmouth center ($35 each way). Bus stop is directly behind the Inn on the Square, short taxi/Uber drive to other hotels.

Location at Logan: Peter Pan buses depart from Boston Logan Airport's lower level (arrivals) outside of Terminals A, B, C, and E. You can find the bus stop by following the orange and white signs for "Scheduled Bus". The bus will pull up as close to the doors as possible, but it's not allowed to park at the curb, so passengers should watch for it.

https://book.peterpanbus.com/#/purchaseflow/departschedules

Departs every 1.5-2 hours and is a 2 hour ride.