iPhone 4 dilemma

I'd suggest getting it replaced by Apple, you might get <6.1.3, but you might not.

And I believe you can jailbreak the iP4 on 6.1.3 http://www.redmondpie.com/jailbreak-ios-6.1.3-with-sn0wbreeze-2.9.14-how-to-tutorial/

 

Yeah sadly. Maybe save your 6.1.2 blobs, just incase you can downgrade later on.

 

You suggest him to save his blobs of his old phone and use them on the new one?!? Smart!

 

Oops, chill out? He can't even use them for anything dude.

And still save them incase you get the button replaced as opposed to the whole phone, or decide against bringing it to the Apple Store.
Better safe than sorry.

 

Nobody will replace any part but entire phone at AppleStore. Policy of Apple...

 

What's more important to you, having a fully-working iPhone with stock iOS, or a broken iPhone with a jailbreak?

If you're considering another phone anyway (whether Apple or otherwise is besides the point), having a fully-working iPhone with stock iOS means you can sell/gift it to someone who may not care about jailbreaking. A broken phone is just a broken phone.

It's also not quite clear whether you have a current jailbreak, or are considering a jailbreak in order to avoid 6.1.3. Maybe, after using 6.1.3, you'll decide it's something you can live with.