Is it possible to use the same RJ-45 connector?
No, in general, it is not possible to "un-crimp" an RJ-xx type connector.

For one thing, there's no way to physically grab the terminals and pull them away from the wire without destroying the plastic housing.

And even if you could, the sharp edges that are required to get a reliable gas-tight connection will have been somewhat blunted by the first usage, and wouldn't be trustworthy in re-use. This is the same reason we never re-used wire-wrap sockets.