I agree with Luci3r.
First things first: updating is not needed. Games may claim that "an update is needed" but it's a flat out lie. If you're on 4.1, there is simply NO REASON AT ALL to update anything but your IOS'es. However, as the only way to play the game is by applying, you won't notice that unless you install a hack that prevents the popup. That'll be priiloader.
Second: bricking your wii with a regular update is unlikely, even if it was modded before*. The official update will eliminate some homebrew, though, so rehacking may be needed...which is another reason not to update.
Third: okay...you updated/remodded your wii recently. Nice. Assuming it was done with a quality guide (e.g. modmii) and your wii can handle disks, then it should be fine. Neogamma is the best disc loader out there, so that should play things nicely. Using the disc loader won't work unless you installed darkcorp...and darkcorp in itself is not something I would recommend.
A small hint, though: for the last couple years, using an USB loader has gained far more popularity over backup disks. It loads faster, is more convenient, and generally more stable than disks (the wii's DVD drive seems a bit like the part that is most likely to break). Oh, and for larger volumes, it's cheaper/game.
*the two reasons I can think of are the following:
1. if you have a hack enabled that forces your system menu to use 249 (but why would you do that in the first place?)
2. if your wii was a region changed Korean wii (not likely if it was bought from a retail store...or outside Azia).