I believe it comes out as "Xristos rajdaetya, Slavyte".
Nektarios, both the Roman and Slavic alphabets are derived from Greek, so in your case it shouldn't be difficult to learn the alphabet quickly. I'm afraid, however, that Russian is not read phonetically as written as much as is Greek, particularly with vowels. If Russian is anything similiar to Bulgarian, there will be much in the area of rules on the subject.
Merry Christmas to the board's old calendrists.
In IC XC