I took the black a long time ago.
See leather watch strap would probably need replacing every 3 - 5 years due to wear and tear or sweat rot depending on the person who owns it. Therefore identifying the strap may be pointless. Your objective is to identify not the strap but the watch face/mechanism itself. As pointed out by Pike, quartz watches are seriously common. Pretty much every single watch out there is a quartz watch. Those with Roman Numerals are almost equally as common, it is actually rarer for a quartz watch face to have a full set of numbers 1 - 12. Far more common for it to bear the 12, 3, 6 and 9 with the rest of them as "ticks" on the screen or as numerals since these often fit tidier on to the dial or look better.
The size of the watch mechanism/face would help too you say it had a thin strap on but as pointed out the likelihood of that being the original strap is nil. If it was truly his grandfather's watch then it would one assume be in the region of 50+ years old. Even 40+ years old we're talking an average of 8 - 45 straps minimum.