Expect the offensive playbook to be very similar to Charlie Weis'. While in Cleveland, Davidson wasn't able to run "his offense", very derivative of the Patriots' system and expected to be using the same playbook. In the NFL and to a point in college, offensive systems are so open to being used in various ways and written coherently enough that coaches will take the systems they liked working with, and do minor chances at most. Even the West Coast Offense, a widely used system throughout the NFL, is largely intact from the 49ers days in the late 80s and early 90s as Bill Walsh finished the system and Mike Holmgren slowly updated it. Holmgren, Mike Shanahan, Andy Reid, Steve Mariucci, and a host of others still use literally the exact same playbook.
And it's expected the same of Davidson. That was likely a selling point (besides the unstated, but expected, recommendation of Davidson mentor Charlie Weis himself, a close friend of John Fox'), given the grumbling of star WR Keyshawn Johnson, and to a lesser point Steve Smith. Smith is due an extension, and Johnson has considered retiring. With both, the point is somewhat clear - they both want to spend the greater portion of the offseason in Los Angeles with family and friends, in their homes, rather than in Charlotte for a few weeks learning a new offense. Johnson, specifically, had gone through a number of offensive changes (learning new head coaches, offensive coordinators, playbooks/systems, and quarterbacks) in his career, and hasn't made a decision to stay.
With Johnson having played under the Weis system before, it's expected the offense will be nearly identical in structure, verbiage, and so on, just with a different coach and different tendencies/playcalling. That would minimize the learning needed for Johnson specifically, and would cascade into quick learning for Smith. It's entirely possible that the pair might be expected to meet with Davidson in LA for a few days over the offseason and expected to be in with the rookies during training camp (rookies are expected to report early).
With the playbook the same, it might not be right to expect the same wide-open philosophy with the team as with Weis. 3 WR sets will be out there, but 2 TE sets will be just as prevalent. FB Brad Hoover may be seeing less time in the offense.
Hopefully, the over-cautious nature of the offense will go a bit. The changeup from being a "draw on 3rd down" to "let's throw deep twice in a row" team really hurt Carolina at times, and while field position is fine, getting first downs should be the concern. A better, more powerful running game as well as a little more varied passing attack may keep the team from intentionally stalling drives by decision-making.
The TE should be involved. With Davidson running the offense, Cleveland's Kellen Winslow II had 89 receptions. It'd be nice to see the team settle on one TE, as well.
With Jake Delhomme a proponent of the armband playbook messaging system, I'd expect the team keeps that facet of the Henning system.