Was trying to make homebrew content where you gain proficiency in an Artisan Tool of your choice however I notice on the drop down list some of the Artisan tools from the PHB are missing.

Cook's utensils

Weaver's tools

Disguise kit

Forgery kit

The disguise kit and forgery kit are tools but not artisan’s tools, the other two are listed. Is your character already proficient with cook's utensils and weaver's tools?

Character is not proficient with cook's utensils or weaver's tools. If you make custom item/feat etc and add one of the options is proficiency with an artisan tool on the drop down list those 2 options are missing.

Do you mean in the homebrewer or on the character? Because both are listed in the drop-down in the homebrewer:

 If you mean on the character, please post a link to your character sheet so someone can look into it for you.