I advise checking with the local UKCA in which ever town you are living in. You will hear about good workmen both Cypriot and British along with several other nationalities. Ask there if they can put you in touch with someone who has had work done by a painter, electrician or whatever you need. There is possibly more of a problem now because many believe they no longer need work permits to work in Cyprus since joining the EU. I am not an EU fan so am not sure if it is true. I would have thought they still need to be registered in Cyprus as a worker to pay tax and insurance.
When I worked there first it was as an Alien but I became a Cypriot after my marriage and therefore no longer needed a permit. I know good and bad workers of many countries. Rarely do you get a good job done on the cheap unfortunately is a very true fact.