Modern Vespa

Is this shock rebuildable? I think it's the stock shock but aren't sure. Stella Atomic Fireball.

Best as I can tell everything on the suspension is tight and solid but the bike has a very disconcerting wobble on light deceleration, like coasting from over 40, and bumps make it dance sideways worse than my v90. I figure shocks might be a good place to start.
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Oh yeah, and I've been riding the Stella and v90 way more than my Dyna lately. Knocked the dust off the Dyna today. It's so much easier to ride than a vintage Vespa, lol.

Doubt there's rebuild kits for it. Be sure to replace with a shock made for disc models (YSS, Carbone, Bitubo, SIP all make some)

That is an o.e. Stella front spring/shock unit. In my experience, they are third-world junk. When I got mine, it only had 1500 miles on it. The springs/shocks looked like new, but they were useless. As far as I could tell, these suspensions rely heavily on compression damping and the damping already was shot. You can spend a lot of money on replacements, but I just got a pair of the Carbones from Scooter Mercato. They were a huge improvement—definitely good value for the money.

If you get new ones, try to resist any urge to crank up the spring preload. You don't need it unless you are quite heavy or riding two-up, and even then you probably only need it in the back.

Those are pure trash. You can get for better for a decent price.