Partly: your outside IT company should keep sign-in, devices and security for Claude. The monthly work on skills with your teams fits their contract badly, and you can test whether yours is an exception.
For most 40-person companies, Team. Both plans charge the same seat price, so the choice turns on how usage is paid for and whether you need a feature only Enterprise has.
A Claude skill is a written recipe Claude follows for one job, and Claude opens it only when a task calls for it. The person who does that job best should supply what goes into it.
Find out who already pays for Claude on their own, collect the skills they built, since skills do not move, and let each person decide what comes with them.
Choose a plan, agree safe settings, write company instructions, build your first skills, connect your tools, name AI champions and train your people. Then decide who approves changes once people start improving it.