i have a bottle of Pavidone-lodine Solution for scratches, thats good for scratches.

get a sharp nail clipper, do not use your old one.
Ask someone to help you, it is way easier if someone can hold the kitten.
Dont hold it up to high, it might panic, hold the torso so the kitten can still reach the floor with his back legs. Clip the nails one by one, but take care, never to deep as it will hurt them and might bleed even! cut them horizontally, not vertically or you might damage the claws.
They will fight for sure but will get used to it after a while... actually will never get used to it but they will get used to you and will not scratch or bite you any longer when they get older.
you can use gloves for the holding hands, might save you some trouble.
Dont feel to sorry, no cat ever died of trimming.

they act like you are killing them but as soon as you let them go after you are done they will not run away, will play and act normal as if nothing has ever happened.
Same with washing them.
Small cats i wash in a clean litter box i no longer use, once they are grown i take them with me in the shower, close the door and shower them. they can not run away there and i dont need to hold them. the first time they freaked out but now they are super tame every time and bear it with patience even attempt to play sometimes. Water will not kill them and will not make them hate you, they might fight and scream a little but after you are done they will stay your best friend.