I am happy that you found a replacement. Do not remove or loosen the lines on the AC cooler in front of the radiator. I think that you can get the radiator out without removing the AC stuff.
Remember to change both the antifreeze and the transmission fluid after your repair. Hopefully, this will fix the other problems with the transmission because antifreeze in the transmission is not good.
There is a good repair manual on this site that may help with your repair. I don't know if you know where it is at. I have used it many times to help repair my RAV4. Here is a link: https://docs.google.com/folder/d/0B61gpLoGBEPNcFlmSTI3aUFhYWM/edit?pli=1&docId=0B61gpLoGBEPNazBwdGNFMFh4c3c
A member named Pim has a link on his profile page of a manual also.
Good luck and keep us posted.