Convert centre positive battery pack into centre negative?

[Big Bob]

Hi, I'm going to be busking with my electric and want to use my delay pedal. Unfortunately, it chews up batteries so I have bought a 12v rechargeable power supply (much greater aH rating than 9v units) and a 12v to 9v stepdown unit. However, the power supply has a centre-positive barrel plug. Can I simply cut the wires, reverse them, solder and re-insulate or is there something else involved? Alternatively, are there cable adapters I can just plug into to reverse the polarity? Hope you can help!

[induction]

Big Bob wrote

Can I simply cut the wires, reverse them, solder and re-insulate ...?

Yup.

[Big Bob]

Thanks for that extremely concise and to the point answer!