Unfortunately you absolutely need some way of booting into Swiss to run backups from the SDgecko.
I've made a couple of portables before and there's a few things to know.
Batteries should be the most expensive part of your build. Use quality. The Gamecube can run at about 11v with it's normal regulator, but if you use 'Zenloc's Custom Regulator', it can use 7.2v, allowing you to use higher capacity, smaller li-po 7.2v batteries. You need heavy electronics knowledge. Capacity? Higher the better. As long as you can make them fit.
You absolutely need a way to boot it into swiss to use the SD Gecko. This means a Viper GC, Wiikey (copies called WASP Fusion were made) or a WODE. You can use Wiikey's own menu, but it's better to autoboot into Swiss so you don't need that silly switch to trick it into thinking it's closed. Gamecube has no IPL exploits like the PS2 does, so you can't boot swiss from the Memory card either. You either need to keep the drive with a XenoGC (or a wii drive if you're adventurous, they apparently work with the proper wiring and power) or you need a replacement chip like a Wiikey or WODE. They're hard to find now, so unless you download the source code for the chips and make one, you have to pay out an extravagant amount for one.