My memory of the sunvisors is that to get to the 'gubbins', the centre cap prises out, leaving a couple of screws which hold the bracket together, clamping the visor 'stem'...... by removing those screws and lifting out the visor you have 2 options,
(1) thicken the stem with some gaffer tape
(2) throw it in the garage.
I went with option 2 about 15 years ago and haven't looked back. It really improves my view out the front (I'm 6'2") and it was never used anyway. I only tend to drive with the roof down, and then the sun just comes in the top, and if it is up, then it's peeing with rain and I don't need a visor.
As Pete says, a cap (I'm obviously much poorer than him as I'm making my Lotus 60th anniversary one last) and a pair of sunglasses and your sorted.
