Hello,
If you are refering to the throttle control cable then any good local garden machinery agents should hopefully be able to help...most will stock a range of throttle cables to suit various makes and possibly some more universal types that can adjusted for length to suit older machines that are no longer supported for spares by the original manufacturer...I'm generally thinking here of a rotary type mower. The length of travel of the cable on older rotary type machines was fairly universal..it was just the overal length of the cable that varied.
If you mean the OPC control "dead mans handle" cable...then they appeared after my time working in the mower world so I would not myself refer to them as an old mower

and I don't know how universal their fittings may be.
Can you post a photo of your mower.??..I might then be able to have stab at a make/model...which may or may not help.

..but would satisfy my curiosity and might send me on a reminiscing trip
All the best,
Clive.