Have the car painted and apply kwa TIMS for a change of particulars. You will be required to book and take the car for inspection. The particulars(new colour) will be entered under the car after which you will be issued with a new log book.
It “has” to be inspected to regularise everything otherwise utakua na gari ya white but logbook inasoma vingine. Alternatively, talk to Kenyans at NTSA in a “Kenyan” way and everything shall be done for you wewe utaendea tuu logbook.