I'll recommend a Nikon AN-4B Nylon Neck Strap (Black) to finish the vintage look. Using small sewing scissors I remove the non-slip material that comes with the strap. This makes the strap soft, smooth and comfortable. I never hang a camera on my shoulder, only over my neck or across my shoulder. If you hang a camera on your shoulder I would not remove the non-slip material. I believe the AN-4B strap is age appropriate to your Nikon FM. I think I started using them on my Nikon F2As and FM2 bodies and every camera since.
Dave