Having followed one of these nice tutorial videos,
i was looking around the different perk properties.

I noticed that it seems that for the 1H speciality perks
the weapon type (if it's sword or mace etc) is not being
checked. I have the suspicion that if I would take mace perk
(more damage) would alos apply to a sword, and vice versa
the bonus for the sword perk would also apply to a mace.

Can anyone comment if that's true?

Happy modding

I would imagine there's a keyword entered for the different types of weapons.

have you checked under the conditions tab in the perk window (there are several different tabs). at first I also wondered, how the magic cost reduction perks work till I found it hidden as a little condition in one of those tabs.

Yep i checked, still haven't found any indication whether the system checks if it's really a mace or sword.

Anyone can confirm ?

It definitely checks. If you click on one of the perk entries and look under conditions, the weapons tab, it checks if its a sword/mace/axe or whatever.