Mats need to be remove before the bath or they will become worst. Rip them apart into small little knots and try working them out with a comb, sometimes powder can help too. Work large mats into smaller knots and work from the skin side out. Skin under the mat is normally very tender and sore and an infection can occur if left too long. Degreasing the kitty is the best way to avoid mats.
Powder can help absorb some of the grease.
I would suggest Soft White grooming powder between baths. If shaving is needed, contact a groomer or your vet. Many breeders enjoy what is called a lions cut during the breeding season when the kitty isn't being shown. This cut is a shaved body leaving the tail, legs, and maine unshaved. Stains around the whites and bicolors eyes are easily kept white with daily cleaning.