Best Extra Slim Fit Shirts

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You will not need extra slim after your analyst stint

A tailor can slim the sleeves on your shirt for ~$20. If it's a cheap shirt and you don't need an expert alteration, a dry cleaner could probably do it for cheaper.

Twillory's slim fit are pretty good IMO!

You can get decent custom shirts for less than $100. If you're looking for off the rack:

Charles Tyrwhitt Extra / Super Slim TM Lewin Fitted / Super Fitted Bonobos Tailored Fit Nordstrom Trim Fit

Twillory, Eton Slim/Extra Slim, Theory, or Samuelsohn Trim.

Or custom shirts--ask your custom specialist to make an allowance of 2 inches MAX if you want a very slim shirt.

Baby Gap

anything but the untuck it guy, hate that guy

Eton makes the best shirts for the money. Get them on sale all day long under $100. Use lyst.com to search. This is coming from someone who has owned a ton of Isaia, Kiton, etc... too.

I think that is Charles Tyrwhitt super slim shirts

Kamakura makes amazing slim fit shirts

Charles Tyrwhitt shirts are great quality at a reasonable price. They have a wide array of fabrics, patterns, weights and the sizing goes from regular to super slim. As a bonus the shirts all come with brass collar stays. I would recommend buying in bulk as you get discounts the more you purchase in one sitting.

I think you should look for some tailored stuff or at least some customized products so that your requirement can be easily fulfilled when it comes to sleeve size modification.

I've seen some retailers and products on Etsy, CafePress or Hyperfavor sell customizable shirts at around $30. Of course, if your price range is under $100, you can probably find more competent brands. It's up to you.