I would have a go and see what happens!
After 18 years they may be a bit crudded up though.
A liberal soaking of WD40 may help.
And although I can't vouch for the quality, similar replacements are available for around £70. Not cheap, but worth it to save hassle?
https://www.amazon.co.uk/Kelelife-Handles-Widespread-Bathroom-Polished/dp/B07NKX4FGK
EDIT: maybe not, this one doesn't have a pop-up waste and the reviews aren't the best!
Good luck