I’m not 100% about how they teach handwriting in Japan, but as a Chinese speaker, here’s the thing: kanji were traditionally written with brushes, and even how they’re written with pens and pencils today is supposed to emulate that. For that matter, apparently a big reason for why chalkboards are still popular in the three nations of the ‘Sinogram sphere’ (aka Japan, China and Korea, the three main nations where Chinese characters were historically used) is that calligraphy shows up better on chalkboards. That is, when teaching students, teachers can show students how to write beautifully: where to apply more pressure, where to apply less pressure, where strokes should be thicker and so on. In other words, very often, it is from brushstroke-style kanji that most natives learn. My primary school Chinese handwriting practice books were full of those. As natives or descendants of native kanji users, we’re expected to try to recreate the brushstroke aesthetic with our pens and pencils. Even kana books for Japanese primary school kids include variations in stroke thickness that are inherent in that aesthetic, despite the fact that the strokes are so thin relative to their length that they’re clearly meant to be written with pens or pencils:
I agree from personal experience that having realistic pen writing to imitate makes things easier, because many brushstroke fonts are unrealistically ideal, but the main factor that allows one to improve one’s handwriting is explanation of concepts and techniques. I know that that isn’t quite your goal as a kanji learner, but that’s what the best calligraphy books provide. Basic handwriting practice books meant for first-time learners (e.g. primary school children) usually just settle for ingraining the brushstroke model into everyone’s mind as the ideal to aim for. (If you need proof of my calligraphy experience… look at my profile picture. I wrote it myself.)
The general rule is this: if you’re looking at a brushstroke font that is non-cursive (i.e. there’s no sign of any threads of ink linking strokes, and all the angles are nice and regular), then everything you see is an integral part of the kanji. If you want to know what the minimum recognisable form of the kanji would be, then mentally remove all line thickness variation. That’s the answer.
I took a quick look at kanji practice books meant for primary school children, and I came up with these two that I think you might find more palatable (the rest were pretty run of the mill and show stroke order with numbering alone):
This one uses brushstroke-type models, but it’s packed full of information on kanji usage and has diagrams of kanji evolution from Oracle Bone Script to modern script. It also includes stroke order information and occasional comments on things to look out for when writing these kanji by hand. I think it’s excellent for someone who’s studying kanji. The text may be difficult for you to read at this stage, but there’s furigana everywhere and with time, you might be able to use it for reading practice if you want to learn more about the usage and history of kanji. This book is probably also closer to being ‘WaniKani style’ because it goes kanji by kanji and aims to teach the reader about how to write each kanji as part of a kanji learning programme. There’s no space for tracing inside the book, but frankly, even though it’s true that tracing is an ancient and traditional form of calligraphy training, the only way to really get better is to write kanji while attempting to imitate the model yourself, constantly asking yourself why the model looks that way, and why your kanji don’t look like the model. You can just as easily trace over the printed kanji using a ‘sheathed’ ballpoint pen for practice. It works for learning stroke order, believe me.
This one is a genuine calligraphy course for primary school students. I can’t accurately describe it any other way. The author includes instructions on alignment and exercises for the basic strokes and movements. There’s also a brief section at the beginning with hiragana and katakana models. Primary school kanji are the focus of this course, but there are no promises on the number of kanji that will be covered, and the book is not structured like a kanji dictionary as with the first book, but as a series of kanji grouped by the calligraphy concepts that they train. This book will teach you how to write well (if you get through the instructions), and all the models are handwritten with a pen. However, since it’s purely handwriting-focused, it contains no kanji data other than kun’yomi, on’yomi and stroke order, and is certainly not ordered ‘WK style’ (i.e. like a reference book that’s mean to teach kanji).
Finally, you might want to look at the ペン文字 stuff on Amazon.jp, and possibly add the words 練習帳 (‘exercise book’) to make it clear that you’re looking for a kanji practice book.
Between the two books I linked to, I’d recommend the second one if good handwriting with ‘pen stroke’ models for reference is your focus. On the other hand, if you’re willing to accept brushstroke models again (but ones that are relatively plain) while getting lots of kanji information and seeing how kanji evolved, then I’d recommend the first. Take a look at both of them. I hope one of them is what you’re looking for.
EDIT: Oops. In hindsight, I guess the English-language books proposed by @chantellis are more appropriate, but since you mentioned ‘Amazon Japan’, I figured you might want ‘helpful models’ and diagrams even if you couldn’t read much of the text (for now, I mean), so I kinda dived right in. I didn’t think to check if there were English-language books on kanji (whereas of course, there are).