Should I worry about my electrician not being vat registered?
Not at all.

If he is a sole trader it is quite possible that he doesn't turn over enough money to need to register for VAT.  Registration is only mandatory above a certain threshold (which changes every year) and is optional below that.  Most traders who don't have to register won't bother as it saves a lot of tax form-filling hassle.

As long as he has the appropriate qualifications, go with it.

He won't have to charge you VAT so you should get the work done cheaper.