I think the most likely scenario is dealing his contract over to a team with cap space, to acquire the trade exception. It limits the contract that Boston can bring in later on, but provides them the ability to open a roster spot right away, and still bring in a player at the deadline if another team is looking to shed salary (HOU and Phx seem likely in that scenario, if they happen to find themselves out of serious contention and need to get out of luxury.)
NJ or SAK seem likely teams that may be willing to rent their space, both have over 13mil in cap space, and are young teams with eyes on the future. Both wouldn't mind picking up an extra draft pick next year, and if their done making moves and likely to keep their cap open for next year, as long as Boston is willing to foot the bill for Sheed's buyout, would probably be glad to absorb his contract and grab an extra pick, as the only expense to them would be the cap hit his buyout would take against this year (And if they're not planning on using all that cap room anyway, that isn't an issue.)
This gives Boston a 6.3mil exception to use to acquire a player at the deadline. The only downside would be in non-simultaneous trade deals, you lose the ability to bring in 125% of the contract, and salary must match within 100k. Meaning, if for some reason Battier happens to ever be in the conversation, his 7mil would be out of range, and require the Celtics to add a player to match the salaries. That shouldn't be a problem anyway, but it does make things more complicated.
But it opens a roster spot at the start of the year, allowing the team to sign Luke and still allow Gaffney and Oliver to fight for that 15th spot, and promote some camp competition, something Danny is big on doing if possible.