You have to create a .reg file and merge it into the registry. The content of the reg file should be:
The aldebaran at the end is the saved putty session config's name. Note that this registry route will only work fine on the installed version, not on a "portable version". You should manually search for your setting by name on portable versions as it could look something by this:
[HKEY_CURRENT_USER\Software\SimonTatham\PuTTY\Sessions\aldebaran]"Colour0"="238,238,236""Colour1"="255,255,255""Colour2"="47,47,47""Colour3"="46,52,54""Colour4"="0,0,0""Colour5"="0,255,0""Colour6"="0,0,0""Colour7"="46,52,54""Colour8"="164,0,0""Colour9"="204,0,0""Colour10"="78,154,6""Colour11"="115,210,22""Colour12"="237,212,0""Colour13"="252,233,79""Colour14"="32,74,135""Colour15"="52,101,164""Colour16"="117,80,123""Colour17"="173,127,168""Colour18"="245,121,0""Colour19"="252,175,62""Colour20"="238,238,236""Colour21"="255,255,255"
[HKEY_USERS\S-1-5-21-4174247993-4083704086-623223898-1000\Software\SimonTatham\PuTTY\Sessions\orc]You can export your putty keys with this command line string:
regedit /ea new.reg HKEY_CURRENT_USER\Software\SimonTatham\PuTTY