In general if the automatic disconnection device (MCB or Fuse) is set to less or equal to the current carrying capacity of the cable then if it fails it will fail safe.
However there are some exceptions like when the cooling fans fail on a hot oven so we aim to select so that there will not be a failure.
10mm sq cable has a range Reference Method 103# (in a stud wall with thermal insulation with cable not touching the inner wall surface) 32A and Reference Method C* (Clipped direct) 64A so we have no idea of the current carrying capacity of your cable. Thermal setting could be even higher so with for example thermal setting SWA run around outside of the house you would be very unlikely to have a problem.
The other point to remember is unlike portable appliance manufacturers of fixed appliances can stipulate maximum overload size so unless you have a mini consumer unit in the kitchen even if the cable can carry 96A (Mineral insulated clipped direct) likely you will still need a 32A or 40A MCB protecting it.
In other words there are far too many variables to give you any real answer. But look on a cable manufacturers web site and you will get all the info as to current carrying capacity of cable the way you have installed it and also sizes of fuse/MCB/RCBO required for cooker.
Simple answer is yes you can replace the cooker cable.
However you say your then going to use that supply for extras. Unless you fit some automatic disconnection device (Fuse/MCB) then cable from cooker needs to be same size as cable to cooker.
Unless your going to change the supply MCB/Fuse then what is the point?
I will guess your trying to comply with part P which allows one to replace but not make a new circuit. I don't care about part P. What you will need to do is fill in either a minor works or an installation certificate really should be latter as you will have two sets of readings but if you want to avoid filling in an installation certificate you could fill in two minor works.
Either way you will need to fill in the tripping time of RCD so one will need fitting somewhere. You can use RCD FCU but I really can't see why you want to fit a larger supply to cooker and then take to shed rather than just take supply to shed.
If you explain what you want to do then I can advise.
It is near impossible for a DIY guy to follow rules to the letter as he will not have the equipment required. I am not saying don't do it but you may need to adopt different methods to what an electrician would use. I think the RCD FCU is the DIY man's friend as it means when you have not measured the loop impedance you are unlikely to exceed the values permitted.