Creating a SQL schema with a "Secrets" table and maybe some audit logging and organizational extras should take a seasoned developer ~30 minutes. Throwing a CRUD web app on top of this and making it accessible to your employees - maybe another day or 2.
I really don't know why you'd risk this sort of stuff with a 3rd party. It just boggles my mind. What are they doing that you can't do? Even a 3 person startup can probably find time around a weekend to knock this out once and for all.
Edit: clearly I missed an important point. We don't care about browser integration. I am not going for 1:1 feature replacement. If you seriously believe "a safe place to keep internal text" is an extremely hard problem that absolutely must be outsourced, I don't know why you would even be involved in technology.