An actual 30 watt iron will handle desoldering a keyboard, IF it's an actual 30 watts and not a 20 marked as a 30.
Beware watt ratings, and brand loyalty.
Years ago, I had a 35 watt Weller pen, would get through 14ga wire without issue, and 12 with some effort. Bought several 30 watt irons and even a 70watt iron and yet none came close to that Weller. I've seen 90 watt irons that couldn't handle 14ga wires (wtf), and I've seen expensive irons with bad tips that couldn't handle 20ga wires. A few years back I decided to replace that Weller with a newer one as the tip was ground to almost nothing and I couldn't get it out to replace it, it is not as good as it used to be. Same Wattage, same model, but Weller was bought out and quality has gone downhill.
Basically, research (more than just Amazon because those are rigged to hell and back), because ratings are pretty useless really, especially since the Chinese have flooded the market with garbage. One popular Hakko knockoff now has something like 5 revisions and sells under 20 different names. Some electrical experts even deemed them flat out unsafe and likely to burn down your house, while others are halfway decent so you need to research before you buy cheap.
If you are starting, a cheap Weller pen works better than other junk in that price even if it's not as good as the older model. I still like the bulb suckers more than the button ones (which VARY a TON in quality and price), the bulbs are simply easier to use (you don't have to be fast at getting the sucker into place, it's already there). If you want a better iron, step up to the Hakko 888d. I'd avoid the Weller equivalent, we threw ours away after something failed and no amount of research could identify the issue for certain, it was either spend 50% on a gamble or spend 100% and get a better iron, we chose the latter. We eventually bought a second Hakko it was so good.
By the way, bigger tips are actually better, they maintain heat better and can transfer more into the joint quickly, so you actually want to use as large a tip as you can for the job. On an old keyboard where you are desoldering switches size isn't really a problem, it's when you start doing SMD that size becomes more of a problem.
Oh and braid is a pain in the neck, make sure it's pre-fluxxed or it will be a nightmare and thinner is better.