The OP is a pilot with a take off clearance, not an ATCO. Unless there was a particular reason to assume the wake risk was increased then the pilot can assume that the tower has it covered. Wheels up to wheels up!
Well I think this is another one of those cases where two parties both have the responsibility. A bit like being vectored when the PIC still has responsibility to maintain situational awareness. Or when VFR the right of way aircraft still has a responsibility to avoid the collision.