You should not wipe a toddler when changing just a pee diaper, unless it is a wet pee diaper from overnight.
Wiping a toddler when just changing a pee diaper is not recommended as it can actually cause more irritation.
You don't have to wipe a baby or toddler when changing just a pee diaper.
If your toddler or baby has a saturated diaper and the skin got wet with urine, then yes you should wipe that pee away.
However if the diaper is just wet and not overly saturated and the skin is dry, then there's no need to wipe the toddler or baby when changing a pee diaper.
Although if using cloth diapers, you should wipe the toddler or baby even if only pee, as cloth diapers don't pull the urine away as good like disposable diapers do.
But with modern disposable diapers, the disposable diapers hold the pee away from the skin, so the toddler or baby does not usually feel wet.
It's actually recommended that you don't wipe your baby or toddler after every pee diaper as doing so could actually cause irritation and lead to rash.
After a heavy or long soaked pee diaper, such as from an overnight diaper, it's best to wipe the baby or toddler in the morning to clear away any urine.
And of course if the diaper is poopy, then always wipe the baby or toddlers bottom thoroughly to remove all poop to prevent diaper rash.
Wipes can also cause irritation and overusing baby wipes, especially with fragrances and chemicals can irritate baby and toddlers sensitive skin, especially if there skin is already raw.
You can also use a damp washcloth to quickly wipe them down.
Urine itself is sterile and does not contain germs and is not a strong irritant until it has set out in the air for awhile.