Sounds quite a find. The DSOTM is 21mm lug width, the 105.003 is 19mm. I would personally want wear it on an authentic bracelet or strap for the age of the watch.
Good to have some provenance. What year does the Cal.321 serial number date it to, and what do the papers have as the date of delivery? I'm wondering when the 1035 bracelet was supplied instead of the 7912 or 1501.