Is there any non-enchanted Staff in Skyrim?

No, staves can be neither enchanted nor disenchanted.

If you're on PC, you can use the Creation Kit to either create a new staff or customize an existing one (Unique staves are good candidates, as modifying them will not change the ones NPCs will use against you).

With Dragonborn, you can craft staves, but they are the same staves you could find or buy elsewhere - you cannot create custom staves.

At the moment, no mods appear to have been developed that add this functionality.

You can make some conjuration staffs at the Atronach Forge, but there's no in-game ability to do much beyond that. As others have said, there's no way to disenchant staffs or make staffs with custom enchantments.

http://www.uesp.net/wiki/Skyrim:Atronach_Forge

No.

I'm sure there are several mods by now that allow this, but in the base game, there is no way to create your own stave.

There are some unenchanted staffs in the qasmoke editor's test cell, but you need to be on pc

In the Dragonborn DLC, By completing the "Reluctant Stewerd" quest for Neloth in Tel Mithryn you gain the key to access his Staff Enchanter. Which uses Heart Stones in Combination with the spell itself and an Un-Enchanted Staff which comes in various types, e.g. Un-Enchanted Alteration Staff. All Un-Enchanted Staffs can be purchased from Neloth.

Just to Be clear, you can't enchant staffs without the DLC