Yep, don't try to solder anything on a battery, but some glue and if there is still place some electric tape.
On both battery (the old and the new) you should find a schema explaining where is the + and the - so you know where to connect the wires.
Ideally Astak will probably sell original batteries for cheap -like $20 shipped-.
On the other hands the batteries photographed by RobertB looks like your average cheap Chinese battery, you can usually get better capacity and lifespan from original batteries from Nokia or any other serious manufacturer, or from a decent supplier like Mugen Power.
And yes, opening the PRS-505 and changing the battery is quite easy too, you unscrew the bottom and the top and that it's, it's a clean aluminum design so you don't have to force open plastic snap to open the case like with devices made of plastic. Batteries are available on eBay too.