This is exactly what weapons allow you to do.
Most melee weapons do their damage based on the base hand damage of the minion.
This additional damage is in addition to other hand damage cards played that increase, or decrease, the minions base hand damage. Playing a Torn Signpost increases the base hand damage to 3, allowing a bastard sword equipped minion to do 4 damage. Unfortunately, the damage done by melee weapons is NOT hand damage, it is weapon damage. This makes the strikes vulnerable to immortal grapple, which excludes any strikes other than hand damage. Another strategy that is offset by melee weapons is changing the hand damage to aggravated.