I modded my WII without using a soldering iron. So it definately is possible.
Just order one of the pre-soldered wii-clips on offer. You can choose from a variety of chips (D2CKey, D2Pro, Wasabi, etc.). Just be aware that some of these still need you to solder something in your WII, or on the modchip for region-free support.
If you happen to have an older WII then you can get a key-clip or free-clip. They are absolutely solder free, but do require you to program the chip with your PC.
So, Shonosuke, to answer your question:
No, modding does not require soldering anymore. At least, not in all cases.
Cheers,