No, based on the versions that Apple is still signing your options are staying put on iOS 4, upgrading to iOS 6.1.3 (not sure why Apple is signing that for the iPad 2, but it is for now) or iOS 9.3.5. iOS 6 is missing some of the features of later versions of iOS, but it does run smooth on the iPad 2 and is an upgrade from iOS 4 at least. iOS 9 is, as I understand it, at little sluggish on the iPad 2, but still usable and will have much better app support. Choice is yours of course!
EDIT: Wait, I just discovered a loophole that will let you install iOS 8.4.1 on your iPad 2. Once you've upgraded to 6.1.3, iOS can't be upgraded directly to iOS 9.3.5 OTA, so if you attempt to upgrade OTA once on iOS 6.1.3 it will give the option to upgrade to 8.4.1 first (note that this will not work if you upgrade via iTunes). I'm going to try it on an old 4s I still have around!