My house still has rubber coated wiring upstairs
When it was still available, that type of wiring was given a 25 year lifespan by it's manufacturers.
It isn't a matter of it needing replacement now - it should have been replaced 30 years ago.
Tests on it will reveal nothing. The insulation resistance of rubber does not deteriorate over time - the material just becomes brittle and eventually turns to dust, leaving the bare wires exposed.
Unless the entire length of all of the wires can be inspected, there is no way for anyone to say that it is safe and suitable for continued use. Even if that was somehow possible, you can't avoid the fact that it's been in use for more than double the expected lifespan of the insulation.
I'm wondering if it would be safer if I replaced the old fashioned fuse wire fuses with one's that trip?
If you mean those plug in things which directly replace the rewireable fuses, then no. They both do the same thing but in different ways. There is no improvement in safety.
Installing an RCD may have some benefit in disconnecting certain types of fault before a fire starts, but installing a single RCD for the installation isn't compliant and when that inevitable fault occurs, you will have no electricity at all until the fault is located and repaired.
A fault may already exist, with the result that the new RCD would not even switch on.
If you were considering a new consumer unit then forget it - no one with any sense would install a new CU onto rubber wiring from over half a century ago.