Does the safety on a 745 block the firing pin from the hammer but not kill the trigger, i.e., the hammer still falls if the safety is on and you pull the trigger?

The Models 52, 745, 845, 952 and probably others that I can not recall are all target pistols, not firearms intended for personal carry.
As you have noticed, they have a hammer block, not a hammer drop.

This is so that you can dry fire without concerns about damaging the firing pin due to over-travel when there is no snap cap or similar device in the chamber

According to Wayne Novak, these pistols can have their safeties swapped out for that of a 645/4506 to make them better for lefties and carry.

Thanks for that info. I’m considering one of these at a local pawn shop and wanted to make sure that was normal. I figured it was given that it’s SAO. But it’s rather different from any other system I’ve seen.

You will enjoy the 745. Have two, both with Novak sights. One has over 25K through it, the other 5K. most accurate 0.45 ACP pistols that I have straight out of the box. Will not be giving those up nor my two M52-2s for similar reasons. Dave_n

Have you ever found aftermarket rubber or rubber-ish grips for this gun?

My shooter 745 wears Pachmayr rubber grips from the 645. I had to grind out the left grip for the safety to clear, but I really like them. To the tune of about 40,000 rounds. I need to replace the recoil spring, but it is still an incredible shooter. I have three others, one back up, also with fixed sights plus one with adjustable sights and another that just turned up. Must have been a busy day when that came home.....