The cable with the white clip fits mine and they're Smiths clocks. Add_Gee - you're right, the white clip wont go through the bulkhead,but you have to start at the clocks and feed the
drive end through the bulkhead and into the engine.
It's possible that the old cable you have isn't actually a Mini cable or is perhaps a clubman cable,but they have a wee stalk which clips I thought,perhaps it's broken off? Anyway - I had terrific trouble trying to get one of the new style cables to work with me,but it now does.
Make sure there are as little bends as possible in the cable and lube the life out of the cable inner - I used vaseline lol

Then check that the cable itself is turning when secured in place,by driving a short distance but with the speedo disconnected so you can see the end of the cable.
If you find the needle is jumping ridiculously then you will likely have a bend in the cable,so try and straighten it. If your speedo still doesn't work, it would be time to check your clocks and speedo drive.
PS - Sprite's also have a different cable I'm told,but I searched high and low and those white clip cables are the only ones available.