You are not going to be able to get anywhere without getting an inquiry on your report. That is just the nature of the beast. If you apply through Tesla, they partner through banks such as Wells Fargo and Chase. Which is what you have basically alluded to in this post.
I belong to a credit union and strongly considered going that route but ultimately decided to apply once through Tesla. They placed me with US Bank originally at 2.49%. Thanks to this forum, I found out about emailing Tesla's finance department and asking them to run my report by Chase, who overall seems to have the better rates as of this time. That is how I got my rate at 2.14. So, I figured why not? I didn't think my CU could really compare or it just would have been one and the same.
You should make a profile with Experian (its free so long as you don't sign up for the extras) just to see where your score stands. Then go from there. I would recommend going through Tesla, then ask for Chase if they don't already place you with them. The online application was a breeze.