Wilsons Confidence Interval Query

I have a proportion which needs to be x 1000 rather than x 100. Normally I would use Wilsons confidence intervals. What will be the consequence/error of using a Wilsons in this situation. I.e 10 people have an illness out of a total possible of 700. Instead of using the value 1.42% (10/700 * 100), I want to use the value 14.2 per 1000. I've asked my colleagues and I am getting differing answers. Some have suggested Byars but I don't feel that's correct - as it's not technically a rate (i.e. no person time in the denominator). Could anyone advise please?