Is there another special word for a small hourglass which is not for one hour but for a less period of time, 10 minutes or even 30 seconds?
As far as I know, an hourglass that measures any other length of time can also be called an hourglass. You can specify ten-minute hourglass, for example. Here's a description for an hourglass sold online (my emphasis):
This unique hourglass puts a scientific spin on the sands of time. A magnet in the wood base interacts with the ferrous sand to produce mesmerizing, temporary stalagmites in the lower chamber of the glass. The natural timer magnetically marks one minute and makes a great gift for gadget-loving co-workers, dads, teachers, or your own desktop. Made in China.
That said, you could call them sand timers, among other names:
An hourglass (or sandglass, sand timer, sand watch, or sand clock) is a device used to measure the passage of time. It comprises two glass bulbs connected vertically by a narrow neck that allows a regulated trickle of material (historically sand) from the upper bulb to the lower one. Factors affecting the time interval measured include sand quantity, sand coarseness, bulb size, and neck width. Hourglasses may be reused indefinitely by inverting the bulbs once the upper bulb is empty.
Then, you could say ten-minute sand timer, for example.