Will re-plating 18k white gold ring affect the diamond?

Not at all. It is done all the time. Find an independent local jeweler and they should be able to help you.

No rhodium (which will be the white plating) doesn''t stick to diamonds, so you ring can be plated as it.  No removing the diamond or anything like that.

The Rhodium plating only adheres to the gold and will not affect the diamonds. However, I will say that before Rhodium can be properly applied to the ring the white gold has to be sanded and polished to make an even coating. This is a good opportunity to have your prongs checked for wear and make sure everything is in good shape for your ring to securely hold your diamond(s).