Here is a video (basically for outdoors) that shows how to Prune a Cucumber plant. It also shows where the suckers are and the tendrils
It is okay to prune cucumbers.
Prune cucumbers throughout the growing season. Watch for new growth points and get rid of them while they’re under 2” long. Additionally, be on the lookout for damage and disease which should be removed immediately.
Young cucumber plants may get ahead of themselves and flower while they’re still small. Clipping off the lower flowers redirects the energy to stem and leaf growth, leading to more fruit in the future.
Lateral shoots, flowers, and fruit that develop on the lower 5-7 leaf nodes should be removed. This is especially important on seedless greenhouse types of cucumbers, as they can support only one fruit per leaf node. If more than one fruit develops, remove it. Find more on this Here -