There won't be a relay for the lights. There isn't really a fix for this issue, at least not one that you can know is reliable, other than to add a relay, there's simply to much current being drawn through the switch for it to be reliably safe.
It's not the steering wheel you need to remove, the boss needs to come off as well, which you either need a puller for or you need to take the steering column out as well.
You should have a Google of relays and make sure you understand what they do, how they work and how they're wired, if you understand relays then the rest is obvious and you'll do a better job sorting this out.
I don't know why they're called relays exactly, but I think they're better thought of as remote switches. You wire them in as if they're the switch for the headlights, but you don't need to be able to reach them from your seat, so imagine an on-off switch under the bonnet. You can run the power from the starter solenoid and earth onto the engine in short lengths of thick cable all neat and tidy with all the high current contained in a short loop of the right wire. Then your existing stalk switch turns the 'switch' (relay) you've just fitted on and off using the existing wiring. You only need a tiny current to switch the relay, so the current flowing through your stalk is much much lower.
It's slightly more complicated than this because you have the change-over function between headlights and main-beam, but you can use the existing wiring to carry on doing the changeover; use a relay for headlights and another for main beam.
When doing this the other thing to bear in mind is that this new loom should be fused and that having a fuse for each light and beam means that one light failing won't take out the other. Your car doesn't have this as it is, so if you don't do it it's not making it any less safe, but it's daft not to fix this risk now while you're doing this. You can get relay holders that feed several fuses.
If you search for "Wired by Wilson" you'll see he sells a loom that covers all this and is designed to fit in the Mini, you could save money doing it yourself, but not enough that it's not worth buying that loom in my view.