Asset Reservation can definitely be done by clients themselves once they login to your WHD page.
To set this up:
1. Enable "Clients Can Search Assets" in Setup > Assets > Options
2. You will have to tick "Reservable" for every Asset record in WHD for those that you allow to be reserved
For clients to Reserve the Asset(s), they can just login to WHD and Click on Assets and do a search for the asset they want to reserve.
The downside of this is that, it will not notify anyone not even an Admin if a reservation was made so will be a double-process for your Clients to create a new ticket for it plus set the reservation in Assets tab.