It'd be fitting and more realistic if there were a config option to disable harvesting wood logs without the correct tool, so that you need an axe; i.e. without the correct tool, the breaking time would be long and you wouldn't get drops.

It can be achieved with PunchMeNot mod. I use it with pyrotech and they fit each other just perfectly!
So, IMHO, you will just "invent a bicycle" having this request done. But everything is up to you.

Also there is Iguana Tweaks Reborn. It has a similar functionality. And if u don't like other features, u can turn all of them off.

I have no intention of disabling tree punching by default in Pyrotech and will not be adding the feature.

Please use one of the other mods specifically designed for this purpose.