If you have Forms Professional, then you're best bet is almost certainly going to be an external database and a lookup on the form.

You could give HR a form or some other process that will update the available shifts in the database, then on the employee side, when you load the form it would pull from the database to populate the list.

When the employee submits the form, run a workflow immediately after that to change a column in the corresponding row(s) of the table to indicate the shifts have been claimed.

You could include an approval task on the HR side just in case you need a way for them to "deny" the request and make the shift available again.

Also, you should include some kind of back-end validation in the workflow to cover the possibility of two people submitting a request for the same shift at the same time.

Alternatively, you could allow multiple people to select the shift and populate that data to a separate table, then on the HR side you could have a single location where they could pick one person to approve, then mark it as claimed at that point and notify the employees.