Ideally, if you're removing the plug (which contains the fuse) then yes, provide it with a fuse. It's just taking precautions. As for the IEC socket... you should only fuse it at 10A IF the socket itself can cope with 10A. Not all IEC sockets are created equal If it's got a built in surge/noise filter, it's more likely to have a lower rating as the components that make up the filter will have maximum current ratings which will be the primary limiting factor.
This is why I suggested you over spec the socket inlet. May cost a little more, but if it can handle 13A, then it's going to be good and more than happy to be fused down.
This is why I suggested you over spec the socket inlet. May cost a little more, but if it can handle 13A, then it's going to be good and more than happy to be fused down.