Sure, police units do fight in wars, one of the first separatists units in Donbas were police, but that's beside the point. When Nazi troopers from Ukraine start attacking, say, a concert in Berlin, you can't expect the Berlin police to fight these highly trained and motivated Nazis on equal footing, can you? What about British police or the Slovakian one? None of these guys have actual fighting experience vs the Nazis with years and years of it.
SWAT units are trained to deal with hostage situations inside buildings and other such places, they lose their experience in street fighting over the years if they have had previous solider training. SWAT units are not the first point of contact as well, it's your regular old beat cop with a pistol who will have to fight these Nazis first. And after many civilians are dead, you need to bring in special forces to take them out, not SWAT, unless they are holed up in a building.
The point I'm making is the Nazis need to lose their morale first before they run out of weapons. If they run out of weapons first, then their high morale will turn towards the EU 'cause they are gonna feel betrayed. And your local police cannot absorb that anger without casualties first.