Hey there, I just created an account so I could talk about this.
Today I've been "troubleshooting" an odd problem with modded Silver Weapons doing "incorrect" damage. I was able to narrow the problem down to Complete Crafting Overhaul, which has an option to increase the bonus damage that silver weapons do to undead/werewolves, which is set to 30% by default. But I was seeing the damage values change in my inventory when changing this setting in CCO. Confused, I looked at how the silver weapon bonus damage is actually implemented in Skyrim.
When you equip a Silver Weapon (or any weapon that has the SilverWeaponScript added to it, from mods etc), Skyrim adds an invisible Perk to your character called the SilverWeaponPerk. Skyrim's Perk system allows Perks to do things such as adjusting how weapon damage is calculated (e.x. Armsman perk). In this case, the SilverWeaponPerk changes the damage formula by adding 20 points but only when the subject is a werewolf or undead. The subject in this case is probably a reference to the target being struck. This is where CCO changes the perk to add an additional X% bonus on top.
What I'm guessing is happening here is that the inventory screen displays your weapon damage by using the same formula as the one used in combat. Except, in this case for some reason the subject is you. If you happen to be undead or a werewolf, that 20 extra damage is added to the display.
So hypothetically, let's say a silver sword should do 10 damage, +20 to undead. You're a vampire, so it shows up as 30 damage in your inventory. Would you actually do 30 damage to "living" targets or just 10? Would you do 50 damage to other undead or just 30? My hunch is the latter. I think the display in the inventory is just another one of Skyrim's many bugs. But I'd love to test that...
Another question might be, from a lore / roleplay perspective, does it make any sense for a vampire to wield a silver sword? Would it not burn their hand, or something?
EDIT: I just spent some time after learning how to use the console to do some testing. I was switching from a steel dagger at 16 damage to a silver dagger with "36", and as far as I can tell there was no difference in damage.
TL;DR: If you're a vampire and you equip a silver weapon, the inventory damage display will be bugged and will show the silver bonus damage as if it was regular damage. You do not actually do more regular damage to non-undead targets.