I agree with graphite... might want to wear your latex gloves. The stuff seems mostly harmless but is attracted to skin and a bother to wash off.
On TR3s & 4s you can just withdraw the inner cable without removing the cable housing from the car or detaching it from the gearbox. Just pull it thru from the speedo end, reinsert same way but twist & fiddle the last bit to get it to seat in the drive on the gearbox. Be aware it will be very messy -- don't let it drag across the interior.
Of course if someone has generously oiled it in the past you may want it all out where you can properly clean both cable and housing.