I know what you mean by sh~s~ye and I think you are right. However, using such romanisations as sh~ye and sh~s~ye will be very confusing for speakers of different languages who don't know what sounds you are trying to express.
Anyway, the pronunction is definitely not like sh~ye, as read with English pronunciation. Of course, many foreigners might say it like that, and you will probably be understood, but if you are aiming for accurate pronunciation, then do not say it like that.