I see it being a number of ways you can skin this, either with Local Profiles, Domain/Roaming profiles or OWA. All of them have their advantages and disadvantages.

Local profiles – Disadvantage: could be harder to manage dependant on your ability to remote into that PC, Local Group and Security Policies No access to shared folders if they move around (unless you have one drive set up for each user) ; Advantage: Local Inbox caching, quicker load times for sign in.

Domain Profiles – Disadvantage: Login times pulling profile down to PC poor, if your current infrastructure has a DC, setting up FSlogix containers for user profiles if cloud based, Group Policies; Advantage: Their files will follow them, consistent user experience between locations and sessions, less expensive hardware required if resources are provided by a centralized server.

OWA – Disadvantage :People just don’t want to use it meaning more complaints, Advantage – More universal UI, very close to feature parity with Outlook.

Personally, I’d do a implementation plan, outlining the different ways you could do this, a step by step guide on how you’d do it, with your costings and hours to implement said solution, and what steps you will need to do to support said solution, and present that to your higher ups to get their approval.

If you work out that it will take you 1 hour to create a desktop shortcut on that local PC to the OWA site, plus a training guide on how to use it, along with minimal ongoing support (other than stuff your guide might have missed) vs 15 or 16 hours to implement the local or domain profile, plus training guide, along with ongoing support, and your higher ups approve one or the other, than you can either enforce OWA, or have a sign off on the bigger implementation when they ask where all your time has been going.