Step 1. Find a very fleshy baby.
Step 2. Remove baby's heart.
Step 3. Remove baby's extra skin.
Step 4. Elevate baby above baby's heart to slow bleeding.
Step 5. Apply tourniquet to baby to stop bleeding completely.
Step 6. Glue newly-removed skin to cat.
Step 7. Pet new, smooth cat.
(NB: Don't tie tourniquet too tightly, as it may hurt the baby.)