Butter and mayonnaise shouldn't have any carbs in them at all unless you are using Miracle Whip, which does have carbs, instead of real mayonnaise. Heavy cream does have some carbs (6.5 per cup), but is limited to only a few tablespoons per day during induction so the carbs from that should be negligible as well.
Be careful with cutting the fats back too much in an effort to cut calories; you actually need fat with this WOE to lose fat, so cutting back too much could actually be counterproductive. The average percentage of calories from fat during induction ranges from 65%-75% for most folks and many find that they lose better at the higher percentage. Contrary to popular opinion, this is actually high fat diet during the early phases, not a high protein one.