I'm on my 2nd character which is a dark elf assassin thief. And I want to improve my ancient shrouded armor and mehrunes razor really high. But I don't rely on smithing. So is there any ways of using alchemy and still get close to the improving skill if you would use smithing?

There are some Enchanted Items and Alchemy Potions you can stack together to up your Smithing. Whether it gets you high enough in skill to allow the improvement depends on what items you use and how low your Smithing Skill is now.

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

i did some rings,necklaces and armors from iron and all in smithing that raise me up like 5 levels in smithing and then if you have a high enchanting skill you can put it to give you more 30 in smithing if you were all the pieces that you can in the armor necklaces and ring that will give you maybe 100 so yeah its a good choice