Summary
I don't expect Martin to be waived, and expect him to be on the Hornets in the '21-'22 season. After only playing in 275 non-garbage minutes across 14 games in the '19-'20 season, Martin played in the majority of the Hornets' games this past season, partially due to Charlotte suffering a lot of injuries at the guard and wing position.

Martin plays hard and doesn't make many mistakes, but his offensive game just isn't at the level it needs to be in order to be a reliable rotation-level player. He's a below-average 35% shooter from three, and really struggles to finish at the rim. A lot of the intangibles are there for Martin to be a decent eighth or ninth man, but he needs to be guardable on offense in order for him to maximize that potential. 
 
Cap Considerations
Martin's $1.8 million salary for 2021-2022 is non-guaranteed, and if he is waived he will become an unrestricted free agent and the Hornets will have no form of Bird rights on him. If he is waived, teams could claim him off waivers, but would need to fit his salary within cap space or an exception to do so, as his contract doesn't fit within the minimum salary exception as it was a three-year contract.

If Martin becomes a free agent, other teams will have multiple ways to sign him as even teams without cap space could possibly use either of the Non-Taxpayer MLE, Taxpayer MLE, or possibly even the Room MLE to sign him. I would also say that in the unlikely scenario Martin is waived and clears waivers, his value will have dropped low enough that he would only have offers for the minimum.