So what can I do to avoid being "that" passenger with bad hygiene?

As you say, the best way to avoid being that guy is to try and wash yourself in between flights. When showers are not available, you can use (scented or unscented) baby wipes to clean your armpits and other exposed smelly body parts. You can wash your face and neck in any restroom sink. And don't forget to brush your teeth. Changing shirt/t-shirt is also very helpful.

Taking regular showers is actually the root cause of this problem. Biologically, taking showers, washing your skin with soap, shampooing your hair, etc. etc. is totally unnatural and it leads to diseases. It destroys your natural skin flora, but far from becoming totally sterile, it causes your skin to get populated by microbes that would normally not be present or not be the dominant microbes. It are these unnatural microbes that will make you smelly if you don't take a shower for a day.

As pointed out here:

When I was a kid, bathtime was a once-a-week affair. We weren’t an unhygienic family – this is just how most of us lived in the 1960s, and I do not remember any horrific body odours resulting from it. By the time I was an adult, I was showering every day. With hindsight, I should have stuck to the old ways.

The habit of taking regular showers does not only make you prone to become smelly, it causes serious diseases. As pointed out here:

The results were incredible. Like most of us in the Western world, the families had far fewer types of bacteria living in and on them when compared with people in traditional tribes in parts of the developing world. One hunter-gatherer community was found to not only have a higher diversity of bacteria, but only one in 1,500 suffered from an allergy - compared with one in three in the UK.

The detrimental effect of excessive hygiene on the skin flora may affect your gut microbiome, problems there have been linked to not only intestinal diseases, but also heart disease and even Alzheimer's disease.

We have to take very seriously the fact that we didn't design the human body, the fact that we take regular showers is not based on any deep insight on how the human body actually works, rather it's based on ideas that are now known to be totally wrong. If you just kick the habit of taking regular showers, then you're going to allow your own body to determine what microbes it wants to have on its skin. But it will take a while for this effect to kick in. The more you exercise, the more sweat your body produces, the faster this feedback mechanism will kick in.

If you are able to convert to the no-shower routine, all you need to do is use only moderate amounts of deodorant, probably less than what you use now after taking a shower in the morning on your way to work. Best of all is that sweating will no longer make you a lot more smelly, the effect is quite minimal compared to people who take regular showers.

Here's what I usually do during long haul flights. I carry mouthwash and a toothbrush and use them when I'm in transit. I then usually go to the duty free stores and try some perfumes :) It also helps if you carry an extra tshirt. Alternatively if you have some of those small roll on deo's, those will help as well