You can use your netbook powered by its mains charger (with the existing battery in place) as long as you like, and with no harm coming to it whatsoever. (There are millions of people who buy laptops/netbooks but never use them powered by their batteries alone).
I'm surprised that your model has only a 3-cell (2200mAh) battery, as the standard battery usually supplied with that model is a 6-cell (4400mAh) one, with this being a suitable replacement:
http://www.ebay.co.uk/itm/like/262483401914
(Oddly, it's slightly cheaper in white!
http://www.ebay.co.uk/itm/like/361596055131 )