Yep, I always use a pair of pliers when changing blades in the Swann Morton scalpel handles.
The 'old' blade is gripped by the pliers, and then deliberately snapped, dropping the point into the tin, then the remains of the blade are removed, again using the pliers, and go into the tin.
The new blade is retained in it's wrapper, held by the pliers, and slotted part way on to the handle, to engage in the groove.
The tip of the blade is then placed against the cutting map, and push down on the handle until the blade is fully home and set.