There is a dog groomer in Paradiso who i am told is good. I am not sure of the name of the road, but rudimentary directions are as follows:

Head along the road next to the lake from Lugano in the direction of Paradiso. When you pass the Hotel Bellevue au Lac on the right hand side turn right (at the traffic lights - the new build all glass building will be opposite you). You are now on the road that leads to Grancia (IKEA etc) and the motorway....after a couple of hundred metres you will see a dog grooming place on the left hand side.

Hope that helps.