Hi Bert,
Switching hands is no problem at all! BSL users will switch hands all the time, depending on a variety of things like where is the person you're signing to (on your left, on your right, or somewhere else), etc.
I realised I am switching between hands too. For example, when I quote a dialogue between people, I use one hand for one person, and the other hand for the other person. Or when I describe a room, I use my left hand for the left half of the room and my right hand for the right half of the room.
So, no worries! 🙂