Is there any suggestions on what on deck launcher can fit this missile? Other than in a tube in the ship?
To my knowledge none was ever designed or considered (since it functionally overlaps with SM-3). Other than having the ground-based launcher adapted for use on a ship, it would probably be "stuck in a tube." And I'm not sure if it would fit in Mk41 at all.
THAAD (as a program) predates the SM-3 program, and was originally a joint USA-USN program. IIRC, the size for THAAD was driven by the need to fit in a Mk 41 VLS cell.
To that end, yeah - you're stuck with some form of VLS with THAAD.