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.
I agree, Solderless Wii-Clips work perfectly fine, ive installed around 10 so far for friends and no problems yet.
Not sure where someone heard they are unreliable, but weve been discussing them in this forum for months now and no problems, if there is a problem, its usually down to the individual not pushing it down properly on the motherboard.
Its a great device and perfect for those who cant solder those tiny points.