I would not trust a vintage leather strap, no matter the apparent condition. Replacing it is cheap; repairing a Deco Rolleicord that plunged onto a concrete sidewalk, or worse over the side of a three story building, would be somewhere between exorbitantly expensive and impossible. This one looks too nice to risk that way.
On a related note, instead of futzing around with trying to clean it and possibly making a mess, send it in for a good CLA to a reputable Rollei tech. They'll clean that up as well while it's in the shop, and then you'll know it is in top form and ready to go for another 70 years.