Hey DrLarsen,
You need to get yourself a Dremel Cordless Rotary Tool. These things are fantastic for tiny, detailed work. There are all sorts of attachments for them like grinding wheels, engraving cutters, polishing accessories, sanding accessories and most important, tiny drill bits.
For the little drill bits, you would probably have to get a set of “collets” which are these little metal shafts which hold the drill bit and the collets themselves are held in place on the tool by a collet nut. Or, you can do like I did and go to their site and get this tiny chuck. If you have ever used a regular sized drill, you know how to operate the chuck. Well, this is the same thing, just much smaller. It cost a little more, but it was worth it to me not to have to worry about getting the right size collet.
I use this tool when I work on my models that require tiny holes to fit together. You could easily drill a small hole in your resin ships without the worry of them breaking apart. I’ve got a drill bit set for my Dremel that covers sizes from 1/8 inch (largest) to 1/32 inch (smallest). The 1/32" bit is nearly the same thickness as the wire of a standard paper clip.
You should be able to find a Dremel at most hobby stores and tool stores.
Good luck with your ships.