Except RAW states "Using a scroll is basically like casting a spell." thus its acceptable for the druid to use a scroll of Enlarge Person/whatever.
Likewise "All wands are simply storage devices for spells and thus have no special descriptions. Refer to the spell descriptions for all pertinent details." per RAW. Further, "Spell trigger activation is similar to spell completion, but it’s even simpler. No gestures or spell finishing is needed, just a special knowledge of spellcasting that an appropriate character would know, and a single word that must be spoken." So all the Druid needs to do in this case is either UseMagicDevice skill or ask a friendly wizard for the correct command word to effectively cast the spell himself.
Also "A potion is a magic liquid that produces its effect when imbibed. Magic oils are similar to potions, except that oils are applied externally rather than imbibed. ... The drinker of a potion is both the effective target and the caster of the effect (though the potion indicates the caster level, the drinker still controls the effect)." so again, potions are an acceptable means for the druid to effectively cast the spell effect upon himself per RAW.
So the question really comes down to whether an enchanted object such as a ring or amulet might work as well. Being the catch-all category, exact details vary by the item - however generally speaking each is either a use-action (like a potion) or Command Word activation (like a wand) which RAW has already confirmed ARE acceptable and effective means of casting a spell, thus SHOULD be acceptable use for the druid.
Its akin to Driving a power-wheelchair, motorcycle, car, or truck in the Modern world. The appearance and speed of each method of movement from point-A to point-B differs, but the underlying rules of the road (rules of magic) and driving (magic) skill involved in applying those rules remains the same.
Casting a spell from memory, drinking a potion of that spell, flourishing a wand of that spell, or wearing/using an object of that spell all APPEAR different on the surface but utilize the same underlying magical rules and thus are interchangeable as far as the druid is concerned regarding getting a specific effect upon himself and companion.
If the druid's ability to share spell effects are THAT overpowered then perhaps the solution is to house-rule they can't in your campaign rather than rework the entire magic system.