spelling it "ha" is actually the proper way to do it.
it's counterproductive to convert every "ha" particle into "wa" because it reinforces bad habits when a student begins to write in japanese. it's easier just to teach that when used as a particle, ha is pronounced wa.
additionally many japanese use zi instead of ji, for some reason or another. it's a throwback to a particular system of romanization that is only really standardized in japan and not used elsewhere.
also when speaking in japanese, students should always remember the vowels ALWAYS sound the same even when combined with other syllables, and generally the consonants do as well.
a = ah
i = ee
u = oo
e = ay
o = oh
the pronunciation of those vowel sounds does not change. if you write "aigo" in japanese it sounds like "eye go". hope this helps.