Yes - that's the part I too have trouble with, and that these products and practices help. They also help the nail itself, but fewer people tend to have that problem.

In my explanation should've said "Splitting/peeling nails, and troubles with the skin around them, are usually due to insufficient oil ...", sorry.

There's no reason why you should trust a random Internet person like me with health advice. But think cost/expected benefit. If your hangnails are anything like as painful and distracting as mine were, trying out a tube of nail cream, moisturiser, and a pair of gloves for a week is a small cost compared to even an outside chance that it'll help. (Unless the use of such products causes big problems for your self image.)