*** Deleted my previous post because it seems to not bear any significance anymore ***
Errm...
I just found out that you simply have to rename the .shipcfg file with a different race-style prefix. So, to make Human style ships available to races using Drengin style, go to your ..\[your user name]\MyDocuments\My Games\GalCiv2\ships directory, open the .shipcfg file with a text editor and save it under a new name with the prefix changed to the new race style. This works at least for template ships (only hull and jewellery), haven't tried it out for ships with components yet.
The race styles are:
S0 - Human
S1 - Torian
S2 - Yor
S3 - Drengin
S4 - Altarian
S5 - probably Dread Lords
Example:
You have made (or downloaded) a ship made for the Human style that's called "TehDrenginSlayer" and want to make that ship available to races using Drengin ship style. Open TehDrenginSlayer.xml and look for the number at the end of the text between the [Model] tags (e.g. UD_TehDrenginSlayer5). Now simply open the .shipcfg file that corresponds to that number (there might be several) and save it under the file name "S3_UD_TehDrenginSlayer5.shipcfg". That's all.
@Kryo:
Did Stardock change the code recently? I'm pretty sure I tried this procedure under 1.11 and it didn't work back then.