As an undocumented (or maybe just unfinished) feature, you can create a shortcut or .BAT file that calls
Paratext.exe -regexpal
. That will start Regex Pal as a stand-alone application.
The reason that it is now normally part of Paratext, is that allows both to be open and for them to respond to each other (e.g. doing a find/replace in Regex Pal will now update Paratext with the changes without having to restart).