IIRC, you would need a MA Non-Res Hunting Permit for Hunting, and for a match, a flyer that shows that you're in the state that current day with your firearms for said match.
But I wouldn't come with a few race guns and no camo, show the officer your hunting license and say that's what you're doing.
What if it was shooting with some friends competitively at a local club? Could you show the officer the clubs schedule where it says Sunday skeet and trap shooting?
"Sanctified competition" - Do you get this designation from your local house of worship?
Attendance at a match qualifies, but you must hold a license form a state, district or territoryt hat does not issue licenses to drug users or felons. Unlike the similar NY law, the MA law does not specify the level or form of match recognition (NY requires NRAor IMHSA), nor does MA law specify the size of the window surrouding the actual match (NY is +/- 48 hours). As it typical of MA gun laws, the details are left subject to interpretation and, in a case like this, there is very little precedent to case law to establish the actual boundaries.
You are out of luck, unless you go the route of obtaining a non-resident MA LTC.
By way of example, folks from Vermont cannot qualify under the so-called "formal target shooting" exception because Vermont neither offers nor requires an LTC or other CCW license.