There are a lot of really great one-handed phones out there, at least one solid one from each of the major flagship manufacturers (Samsung, HTC, LG, Motorola, etc etc). It all depends on which features you are looking for.
Each has its signature/important features, and its drawbacks. You've mentioned what you don't like about the Note 4 - and fair enough - but you are using it as your reference for "finding a one-handed alternative to". In order to find an alternative to it, you'll have to determine the things you DO like about the Note 4 so you can look for another phone with those features.
So what features do you like about the Note 4 well enough that you are using it as your reference point for a good phone? Obviously not the screen size - because you've said the phone is too big. S-Pen? Infrared? Fingerprint reader? What is it that makes the Note 4 the ideal phone for you, "if only it was a little smaller, the bluetooth worked for me, and it didn't lag"