The final consonant of huit is often dropped when it is part of the phrasing mille-huit-cent simply because it rolls off the tongue better, but it would not be a mistake to pronounce it.
This elision can also happen when the word huit is placed before any word that begins with a consonant other than h, or when the word huit is followed by %. Examples from the Office Québécois de la Langue Française:
Éric commencera ses cours le 8 septembre. [ɥitsɛptãbʀ] (uit-sèp-tan-br) ou [ɥisɛptãbʀ] (ui-sèp-tan-br)
Le sondage indique que 88 % des personnes interrogées ont accès à Internet à la maison ou au travail. [katʀevẽɥipuʀsã] (ka-tre-vin-ui-pour-san) ou [katʀevẽɥitpuʀsã] (ka-tre-vin-uit-pour-san)
In my dialect of French spoken in the metropolitan area of Québec, this elision can also be applied to other digits, though is less common to do so in formal contexts. You can read more about it on the OQLF's website. Judging from people's comments, that is not a thing in France.
Note that the pronunciation of the rest of the digit doesn't change. Even if you drop the
t in huit, you should pronounce hui all the same. In the question,
hui was approximated as
wi, but neither are exact. You'll probably just get yourself more confused if you try to rewrite French words as if they were made of English sounds.