Hard one - but if you haven't told headoffice yet, sit down with the bloke and explain CALMLY the ins and outs of it...

If YOU still think it's doable to let him have the time off, as you think you can cope with the workload, but don't want a bollocking from headoffice about letting him have it off, maybe suggest he takes a few sick days? Sure the company won't let more than 2 peeps have the same holiday days, but they can't do fuck all about someone being out sick