I don't see anything in the Diamond Care product care instructions that says that Petroleum (e.g. mineral spirits) or a brush on it. It says not to use "harsh abrasives or detergents" but doe snot give specifics as to what those may be. I would be really surproised if wiping with mineral spirits was an issue, but a dish detergent like dawn will remove wax anyway. But it may take several washings to get a good paste wax off.
They do recommend a cleaning product called Bug Magic, but I don't know if that removes waxes or not.
The best product for wax removal is ammonia, but I would be cautious about using that on Diamond Shield. Try it in an unobtrusive corner first to see if it discolors it .
303 is the recommended protectant, but does nothing for removing old wax.
Invisible Paint Protection Film - Product Care
2004 American Tradition; 2014 Buick LaCRosse
Homebase in the Ocala Nat'l Forest near Ocala, FL