Measuring Current in Coax Cable Using Clamp on Current Probe
AFAIK the magnetic fields of current flowing through the sheild and
central conductor should cancel out

Theoretically and practically they do - the external magnetic field (beyond the shield) produced by the inner conductor current is exactly opposite to the magnetic field outside the shield from the returning current in the shield.
The only magnetic field that exists inside a coax cable is between inner conductor and shield.
This is why coax is so sexy - the outer shield (being a tube) is unaffected by the internal magnetic field therefore, from that standpoint, the shield has zero inductance and, given that the fields cancel outside the shield, the shield can be well and truly regarded as having zero inductance because it isn't subject to any net flux changes that induce voltage in it.

Unfortunately I don't currently have access to this adapter, so I am
going to need to build a new one.

That seems the only route given that (a) it works, (b) you've used one before and (c) the theory is sound. That would be my choice. The 7th harmonic of 5 MHz is 35 MHz and the wavelength is therefore around 10 metres so a few inches of extracted inner isn't going to make a whole deal of difference to impedance balancing or reflections.