From the pictures I found. both the left and right speakers connect to the subwoofer (purple plug), the subwoofer houses the AMP and connects to the volume dongle, the subwoofer connects to the source (green plug).
since the subwoofer is the amp and volume control any unpowered speakers with a 1/8th inch plug will work. provided the impedence and wattage match)
you can replace them, but you'd have to do surgery on the old ones and get the impedence and wattage of each unit. then find speakers unpowered in their own case, and wire them via 1/8th inch adaptor to the subwoofer.
While it can be done it will take work and time. there are no plug and fit replacements for that system.