The device itself can't do what you are after but if you want to spend some $$$, get yourself a managed PDU (Power Distribution Unit) from one of the main vendors (APC, Avocent,Tripp Lite, etc) and not only can you schedule a shutdown but it also can bring the system up from remote in addition to protecting the system from power surges.
If you don't have the $$ to invest and cheap solution is getting an electric timer which can be found in most hardware stores.
What's the purpose for shutting down the unit? Saving electricity in the Lab?
Unsure whether 4500 supports this possible solution, but instead of shutting the switch physically down, perhaps you might be able to use timed based ACLs to block all traffic from 1 AM until some time later that morning. Timed ACLs also, I believe, "know" the weekday so you might vary the schedule on weekends. (If timed based ACLs are supported, you might also just target specific VLANs or ports, so only your student access is blocked. Avoiding physical reoccurring power-off/on might be better on the equipment too.)
We are pleased to announce availability of Beta software for 16.6.3. 16.6.3 will be the second rebuild on the 16.6 release train targeted towards Catalyst 9500/9400/9300/3850/3650 switching platforms. We are looking for early feedback from custome...