First, make sure that the dog can’t physically get hurt. Toy breeds usually have very fragile bones. With time the dog will get used to the slippery floor and he manage to move around in a better way, but at the beginning he’ll be nervous and that could make him fall.
Second, for these kinds of problem the strategy that I would adopt is to use counter classical conditioning in combination with positive reinforcement for approaching the location. That means that you’ll first reward the dog for approaching the place, stepping on the floor, etc.
Step by step, very progressively and with many short training sessions. Then, as the dog approaches the slippery floor and stand on it, the counter conditioning means that he will associate the place with positive events and not with his fear. You could give him some treats or feed him some portion of his meals there.
The two key points are:
- make the dog think for himself and decide to approach and step on the surface (that’s operant conditioning, you reward every tiny step)
- suppress completely the old fear that the dog have, that’s the classical counter conditioning part
This is explained in detail in this video: How to train your dog to get over his fears! using clicker training. That’s for a dog who’s afraid of the kitchen slippery floor.
When dealing with fear problems two things have to be avoided: correcting the dog for the “bad” behavior and “flooding” the dog, that means exposing him to a very high level of fear/stress thinking that if the dog overcomes his fear he will be treated.
That’s the equivalent of locking a person who suffers from arachnophobia in a closed with hundreds of spiders.
I don’t think any sane person would recommend that or would volunteer to be treated that way. In the approach I describe above, you start reward the dog as soon as the level of “stress” is present, at a very low level, say 3 meters from the bad spot.