Кстати, а точно ли нужна справка или самих прав достаточно для обмена?

Вот да, интересно

Вроде как отменили, но хотелось бы узнать точно)

In order to exchange your foreign driving licence you will need: 1.    To fill up an application form: TOM7Δ 2.    Your Identity Document in case of Cypriots or your Alien Residency Permit in case of aliens (original and a copy) 3.    Passport (Original and a copy of the first page with your personal information) 4.    Your foreign driving licence (original and a copy of all pages). (The licence will be sent to the competent authority of the issuing country) 5.    A translation of the driving licence is needed, unless the driving licence is in English or in Greek. Translations are valid only if  are done through Press and Information Office or by the ambassador of the issuing country (original and a copy) 6.    In case of aliens, a valid immigration permit is required (original and a copy, receipts will not be accepted) along with prove of your stay in Cyprus for at least 185 (one hundred eighty five) days within one year. This can be proven through utility bills of Electric Authority of Cyprus or Water Board or a statement of social insurances from the government department on the requester’s name etc.  In case of students, you it can be proven with a certificate of studies from a higher education school. 7.    You have to come in person with your application form, along with all the necessary documents to the district offices of the Road Transportation Department Notices •    In case of you are over 70 years old or your exchange the driving licence for the categories Γ, Γ+Ε, Δ, Δ+Ε, Γ1, Γ1+Ε, Δ1, Δ1+Ε an extra form 153E is also required.

Судя по написанному выше