Modern Vespa

Apologies if this has been covered elsewhere, but I have questions on rear wheel spacers for a 2016 Vespa 300cc Super Sport.

I have two rear wheels:
1. one with the tone ring directly attached to the wheel rim (this was on the scooter when I bought it);
2. a second, ordered later, with the tone ring that screws to the special wheel rim bolts.

Part number for the spacer on the left in the attached photo (on the scooter when I bought it used) is P1848039, according to SIP. I've also seen it listed as 1C002344 in a Piaggio Spare Parts Catalogue.

Part number for the spacer on the right (ordered from SIP) is MV848039.

I'm installing the original wheel (the one with the tone ring already attached). When I use the original spacer (the one on the left) I find the spacer can slide back and forth on the axle about 1/8th of an inch. That's without the right rear swing arm attached.

My questions are:
Is that 1/8-inch space something to worry about?
Will bolting on the swing arm take care of it?
Should I use the SIP spacer instead?

Apologies for this being so lengthy, but I wanted to be as clear as possible.
Thank you for your help.

Once you tighten the swing arm nut, that gap will close up. Went through the same thing and it drove me crazy… Test drive it of course just to make sure