Yes, in principle this will be fine. Just check the outlet at the bottom of the flush valve is the same diameter as your existing valve and it will be a case of simply swaping the two valves. The job will be easier if your new flush button is the same diameter as your old one. I'd suggest installing a new fill valve whilst you've got the cistern apart and use a fresh set of fixing bolts and washers if it's a close coupled cistern.
