I wouldn't bother with a splitting tool, or dematting tool - even their names suggest how damaging they could be to a coat.
The only 'tool' I could recommend to try & split a large matt would be a seam ripper. Be VERY careful though, these little suckers are SHARP!
I have only used the seam ripper on Dakota when she was in coat with terrible under-arm matting - you need to carefully try to split the matt with the seam ripper, then put it away, and work on the smaller matts by hand.
Good luck - hopefully you wont need any tools! (one can dream!)