Having a quick look at the Community Market, it turns out you can use Specialised Killstreak kits on them. As of right now, there are two different Invasion weapons so far that have kits applied to them, those being the Giger Counter and Batsaber, proving that the weapons can have kits applied to them. The item descriptions even show that they have a visible sheen and active killstreaks.

Right now, I don't know whether or not this is the case with the Shooting Star and the C.A.P.P.E.R, though I'm willing to guess it would be. It's unknown at the moment whether the kits used are meant to be applied to the weapons they're a reskin of or these reskins specifically.

Having a quick look at the Community Market, it turns out you can use Specialised Killstreak kits on them. As of right now, there are two different Invasion weapons so far that have kits applied to them, those being the Giger Counter and Batsaber, proving that the weapons can have kits applied to them. The item descriptions even show that they have a visible sheen and active killstreaks.

It seems like the kits used on them may well be blank kits, which is proven by the fact that the Wrangler (the weapon that the Giger Counter is a reskin of) doesn't have any kits at all.