I don't think that's possible. You've got a couple of other options though.
1) Give them a direct URL of the instance config
It will look something like this:
That will save them from having to click through the console to find the right screen and the right instance.
2) Auto start/stop the instance
If they need the instance running on a predictable, periodic schedule - e.g. during business hours, or every Monday, or every 1st of month - you can automatically start and stop it for them.
Here is a simple CloudFormation template that does just that:
Modify to suit your needs. You will probably want to point it to an existing Instance instead of creating a new one; however the scheduler and the Lambda should be reusable.
3) Create a simple start/stop app
If you want to give them a single start/stop button on a screen you will have to write an app for it. It can be a trivial PHP script running on a
t2.nano where this instance will have the appropriate IAM Role with permissions to start / stop the target EC2 instance.
Or if you want to go completely serverless write your app in jQuery, React, Angular or something like that, store it on S3 and make it talk to a Lambda backend that will be starting and stopping the finance dept instance. Again the Lambda will have the appropriate IAM Role with permissions to start / stop the target EC2 instance.
In both these cases you will want to handle user authentication somehow. It may be a simple, shared password right up to a full-on AD authentication through AWS Cognito or similar.
4) Create a start/stop script on their laptop
As Tim suggests install aws-cli on one of their laptops and create a simple
stop-instance script. However if they use Windows (as they probably do) they may freak out if you ask them to use a command line :)
5) Create a self-service menu system
t2.nano EC2 instance create a local user whose login-script will present 2 options:
Finance department server is currently: running
Your choice [1/2/Q]: _
They can SSH to it e.g. from PuTTY (it can be all pre-configured) and simply choose what they want. I've had a similar system for our users who occasionally needed to restart a certain application but I didn't want to give them shell access.
Hope some of it works for you :)
BTW Every time they choose to Stop it you may also want to create a snapshot, just in case...