There is not a good way. If you cut them try to get down to where they attach even gouging out the attachment area a bit. There are dormant respout buds in this area which just pop back out when you cut off a sprout...as you already know.
True cacti love lots of light...direct sun if possible. If the 8 hours is sunlight most any dwarf cacti available in your local Home Depot Garden Center will do fine. If the light is artificial lighting cacti will tend to stretch and get lanky, declining over time.
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