First off, unless you did the softmod yourself and know exactly what was done to it, NEVER attempt an update through System Menu or a disc.
If you don't have IOS58 installed you have to be on SM 4.2 or lower, most likely 4.1. And if you haven't been constantly nagged by the disc channel every time you play a retail disc, then you most likely also have Preloader/Priiloader installed which would block official updates anyway. Updating your System Menu will most likely render your modchip useless. One or two modchips had firmware updates to work past 4.1 but by then most modders had moved to softmods and/or USB loading so hard mods quite being supported.
If you have a Windows machine (or can run Windows programs) use
Modmii to create a guide for your Wii. Put it on your computer answer a few questions it will create a guide and build all the files you need.
There is also a decent softmod any wii guide over on WiiHacks but it can be hard to follow.
What you want to do is:
Use current HBC and a wad manager to install IOS58
Use HBC to load
Hackmii installer to update HBC and to run on IOS58
Use a wad manager or cIOS installer to install cIOSs 249[56] and 250[57] I'd use d2x v10beta52 but d2x v8 should work
*optionally use a wad manager to install updated versions of IOSs used by games (ones lower than 58 not including 36).
If you don't plan on playing from disc anymore, you really just need HBC running on IOS58 and the updated cIOS249.
Some games, like CoD, need a cIOS based off IOS57 or they just black screen when loading so install cIOS250 and GX will require a setting change to load the game with IOS250. Other loaders like CFG or WiiFlow auto select the best cIOS from the ones installed.