If running the script is the only thing you want those other users to be able to do, then I'd go with using ssh keys.
Each user should have their own ssh key, so you won't get into a hassle when somebody no longer needs access. The public part of the key should be put into
~scriptuser/.ssh/authorized_keys
and in front of the actual key, you should add the text command="/path/to/script"
Here's an example:
from="10.23.5.32",no-port-forwarding,no-X11-forwarding,no-agent-forwarding,no-pty,command="/path/to/script" ssh-dss A........
This limits the ip-address that this key can be used from, and it limits what kind of forwarding can be done, and makes sure that no pty can ever be granted when using this key, and whenever the user connects with this key then the script will be run and nothing else can happen.
To add an environment variable, you just add it too to the key:
from="10.23.5.32",environment="MYVARIABLE=whatever",no-port-forwarding,no-X11-forwarding,no-agent-forwarding,no-pty,command="/path/to/script" ssh-dss A........
However, in order for that to work, you have to have the PermitUserEnvironment
directive set to "yes" in the sshd config file. If you can't make that happen, you can instead change the line to this:
from="10.23.5.32",no-port-forwarding,no-X11-forwarding,no-agent-forwarding,no-pty,command="export MYVARIABLE=whatever; /path/to/script" ssh-dss A........