To use the signing tool from multiple computers simply copy the sigtool.csk and sigtool.db file from the bin directory of the JDE on computer 1 to the bin directory of the JDE on computer 2.
sigtool.csk has the private key
sigtool.db has the location of authorization server along with your registration PIN
Now when you run the Signature tool on the new computer if you see a screen saying not registered for any of the 3 types:RBB,RRT,RCR then simply open the sigtool.db file ad make sure it has 3 entries one for each type.
In my case the RBB had a different private key than RRT and RCR, so a simply opened sigtool.csk file in notepad and pasted the private key into it.
Now when I ran the Signature everything worked as desired. Hope this helps.