Just looked at the spec for the ‘crazy lights’… the remote control is RF based so not an easy thing to hook up to SmartThings.
Shame it’s not infra-red, would have been fairly simple with a Logitech Harmony setup.
Only suggestion might be to dismantle the remote control and see if you can solder onto the PCB button contacts.
If you can, 3 double Zwave relays (capable of momentary output) would do the trick, as the remote only has 6 buttons.
I would recommend the Fibaro double relays but they are not available in the US. The Fibaro double switches also have a momentary flash ability, but they would have to be wired up to a bank of dumb relays to achieve dry contact.
I remember someone on here recommending a US relay option once, but I can’t remember the brand.