It's been a few years since I was last there, but if you might visit Ta'Qali (next to the National Football stadium), it's also the Malta Craft Village.
It’s based in an old WWII RAF airbase (including many Nissan Huts), it has an aircraft museum, you can have lunch in the old RAF Canteen, look around the craft shops and see where/how things are made (they are famous for their filigree work) and yes, there are people working wood and I remember seeing at least one lathe there last time I visited.