If the seat is clean and dry, you don’t need a paper cover. If the seat has drops of urine, they will seep through the paper (just wipe off the seat).
Some people worry about contracting a disease from a toilet seat, but this fear is unfounded. As long as the skin of your buttocks and thighs is unbroken, you have no chance of getting a disease from the seat. The many layers of skin form a fairly impermeable barrier; in addition, the skin is laced with certain immune cells that protect against microorganisms.
The most important thing, of course, is to wash your hands with soap and water after using the toilet, since microorganisms can be transmitted from hand to mouth.
