Can you buff movement while wielding a (Golden) Hammer?

After some experimentation:

Movement

Jump ↑ does nothing for height while wielding a hammer. It probably does nothing for jump speed either, but even if it does it’s very subtle.
Lightweight also doesn’t help hammer jump height, but it seems to improve horizontal movement. Perhaps more importantly, it helps you grab hammers before others do. Probably better to prefer it over Item Gravitation.
I have yet to test Movement ↑, Dash Attack ↑ (slightly increases movement speed), Landing Lag ↓, Floaty Jumps, Slow Super Armor/Armor Knight, Braking Ability ↑, the jump/movement/fall speed-related Dojo Styles, or the the Rocket Belt or Super Leaf items.
- I haven’t tested Instadrop or Impact Run either but I highly doubt they work while swinging.

Didn’t test this yet, which might come from any of the following:

That said — do you really need to buff Hammer offense?

Item Gravitation can help grab hammers first, but Lightweight also does, and then helps after getting the hammer. (Movement Speed ↑ may also.)
Unsure about Shield Damage ↑, but might also be moot with the hammer, just like damage buffs.
You can’t get Lifesteal and Increased Hammer Duration.
Savvy opponents may still hit you while you’re swingin’. Improved Escape can help if grabbed, and Franklin Badge Equipped helps against the projectiles that make it past the hammerhead.
Falling Immunity stops tripping from banana peels, down tilts that outrange the hammer, etc. Bury Immunity is too situational.
Super Armor is good, but you didn’t need me to tell you that.
Nothing prevents counter specials from absolutely destroying the hammer wielder.
Strong Wind Resist/Immunity don’t protect against windboxes — not even the Gust Bellows. :(
Giant would be effective if you could guarantee a Hammer spawns early. But you can’t.
Back Shield Equipped will not help very much, if at all.