You can try Japanese Transliteration which will take English words and *transliterate them into Hiragana, which you can hear spoken (lower right hand option). This means it will show you the Hirigana spelling that most closely approximates the sounds of the English word. You can decide how good it is by listening to the Japanese speaker pronounce the Hiragana. For me, most are close but definitely not sounding like English.
As your article says, there is no definition of on in English, the number of on can only be computed by converting the sound to Hiragana, and then recognizing (from the Hiragana site) how many on are represented in the Hiragana spelling.
In Hiragana, either one or two glyphs represent a single syllable to be uttered in the Japanese language. Scroll down in the site to get a complete list.
Because it refers to sounds, you might be able to portray the sound of an English word in Hiragana, but not every English sound can be represented in Hiragana.
For example, the words "chick" or "bat" both turn into two syllable words in Hiragana, sounding like "chi-ku" and "ba-ta", because all Hiragana syllables end in a vowel sound.
I would also say, whatever you write in English trying to adhere to this strict definition of on will likely be rejected as not real Haiku; readers and critics won't care about such technicalities and will count English syllables, which is apparently what the inventors of Haiku were aiming to do in their own language, capture syllables of the Japanese language.