The replacement buttons you will need are 5mm x 5mm x 1.5mm SMD Momentary 4 Pin Tactile Micro Switches which you can buy online in packs of 100 for only a few pounds.
Product links below:
Amazon.com – 5mm x 5mm Momemtary Tactile Micro Switches
Amazon.co.uk – 5mm x 5mm Momemtary Tactile Micro Switches
It’s a good idea to replace the battery at the same time which is a standard 2032 3V battery.