Just this time I will disagree, working on Decca is not the same as other carts, Decca have some odd things you need to know about and they are quite particular to calibrate.
To OP the hum could be a few things, the clips on the slide and the contact dots can oxidise or sometimes the contacts need prising out a bit to get a decent connection. Other reason for hum is the cart is close to EMF, the Decca is not a shielded cart so near a transformer or near a turntable motor that is not shielded again will hum.
The cart will have at least two issues that will need to be addressed to make it work correctly, first for sure the tieback will be slack, if it is slack the armature will be bottoming out and if not then at best you will have music but virtually mono. The armature needs to be in the correct position between the coils and all old Decca will be wrong. Next issue will be the damping rubber that was originally stuck to the base of the stylus holder (what Decca call the cantilever) will have turned to gluey snot and the stylus holder will be resisted correct movement by this goop, most old Decca will need this cleaned up and new rubber to be fitted. When this is done the stylus holder needs to be in the correct position and then the cart correctly calibrated using calibration screws to get correct stereo. Lastly a retip and damping.. Joseph could do a retip but I doubt he would be able to do any of the other things as you need to know Decca intimately and know there querks. It is worth pointing out too that coils on these 40 year old carts co open circuit when you as much as look at them so massive care needs to be taken lifting out coils to do the work. I have spares for this reason and you cant just put a new coil in it must be fitted in same orientation as others, like I said Decca are a bit special. Also worth mentioning that servicing a Decca the OP should get a line contact stylus, but also get the internals damped which will take the cart he has up to super gold specs.
I would be talking to John Wright in the UK and nobody else as there are very few of us who know how to do Decca and even fewer who have spares for them.
Chris