You can enable/disable apps in Tenant-wide settings but i am pretty sure that there is no option for enable/disable Connectors there so i think PowerShell (that you do not have access to) is the way to do it. In this postShrikant Suravase explains how to do it.
Every Connector should be listed under the "Apps" section in the O365 Admin Center -> Settings -> Services & Add-ins -> Microsoft Teams -> Tenant-wide settings. You can toggle them on/off there, but those settings apply to the whole tenant, not individual Teams. There is no feature that enables you to control this per-team yet, you can only enable "no" Connectors or "all" Connectors (as long as they are allowed in the tenant settings).