Buying an iPhone SE New or Refurbished?

I'm planning on getting a new iPhone SE for Christmas, because my iPhone 5 no longer supports the latest iOS version, and I'd like to upgrade without spending $1,000 on a phone I think is too big, and honestly gimmicky. I also personally consider a real home button and headphone jack necessary, and don't want to lose my 4" screen that fits my hand perfectly.

Anyway, Since Apple no longer sells them (for some reason) on their main site, my options are to buy locked to a carrier (A no-no for me) or on a website like amazon. From there, I can go for a refurbished or unopened phone. Here's the problem:

I would definitely rather buy a brand new iPhone, since I know for sure it is in mint condition and hasn't been damaged or tampered with. However, I am concerned that the phone I buy could be 1-2 years old, and if the battery has been sitting dead for that long I'm afraid the battery will be unusable phone will be useless until I replace the battery. This isn't something I want to do, because I tried to repair my iPhone 5s recently and broke it, forcing me to use the 5 and causing me to look for this upgrade in the first place. (On a side note, Apple made a mistake by putting 1.2, 1.3, and 1.7mm screws in the same IO shield and deciding that using the wrong screw will brick my phone. No, I do not own a digital caliper to measure these screws, and no, I will not be told it costs hundreds of dollars to fix my phone, or that I will not receive service because my phone's too old (even though it runs iOS 12).

So my question is: Is it likely enough that a brand new phone would come with a defective battery due to it sitting unused in a package for a fair amount of time (more than 10% likely) that I should look for a refurbished phone and deal with minor cosmetic damage and the risk of tampering/water damage from previous user?