Learning something badly can be disastrous. I self-taught myself to type years before I took a typing class in school. Despite multiple attempts to learn both qwerty and dvorak I still use my invented four-finger method that doesn't allow me to fully touch-type without looking down.
I recently read somewhere (maybe on the Wiki?) that there was a study that didn't find any advantage of classical touch typing over self-learned touch typing, in terms of speed of input at least.
In other words, nothing is stopping you from using your four fingers to type without looking at the keyboard. If you spend a whole day typing anyway, make a conscious effort, for a few minutes every day, to type by guessing where to move your fingers (whichever finger feels the closest or just the most comfortable). If you're like me, you already know where the keys are, you're just looking down to make sure. After a while, you'll see that you can write without looking, no problem. And at that point, it stops mattering if you use 4, 5, 6, or 10 fingers.
I was a 5-6-fingers non-touch typer for a very long time, my input speed was satisfactory anyway, so I didn't feel the need to learn the "proper technique," which seemed like a huge PITA. I was convinced that the proper touch typing is the only way to type without looking at the keyboard. I changed my mind due to a situation at work, where I was explaining something to a co-worker and had to use her laptop for demonstration. The catch was that her keyboard was completely blank. I was stumped for a while, but - having a reputation of a senior to uphold - I said (internally) 'fuck it, whatever happens, happens,' closed my eyes, and just typed. It worked, not 100%, but close enough. The co-worker wasn't impressed (well, she was the one who used such a keyboard, to begin with), but I was in awe. I realized that looking at the keyboard is just a habit, not an essential part of the typing process. Now I type mostly by touch, still use 5-6 fingers, still have satisfactory WPM, and I look down at the keyboard only when I'm distracted or when I have to reach some very rarely used key (like F5 - F9).
To summarize: if your work is based on typing on the keyboard, then the chances are that - after a few years - your fingers already know where the keys are. It's like riding a bike with hands away from the handlebar: if you've been cycling for a few years, you most likely are capable of doing this, you just need to realize it.