Installing gear cable guide on 80s Holdsworth
The little hole looks a similar size to the one in my early 90's steel frame BB. Mine is threaded, perhaps yours is too. Maybe it didn't get masked off by the painter and the thread is under the paint. You could ask the painter if they remember taping it or not. You could check for threading and possibly tap the hole yourself if if isn't already.

You can also get cable guides which have a little solid plastic nub which goes into the hole and there is no screw, it is held in place by cable tension. I'll have a look for an image or something but might be a needle in a haystack. Chances are an LBS or framebuilder/painters will have some miscellaneous ones, you could ask around in person and see if you can find one to suit your frame, designs vary.

Other suggestions, from here include glue (!) and double sided tape to position the guide before cable tension takes over. I don't know how they would affect the paint long term.