First, take on is only an alternative for hire when you're talking about a person (or people), and only in the sense of employment or contracting. You might hire a boat at a boating lake, or hire a car when you're on holiday, but you wouldn't take on a boat or a car. Well, there are probably some very specialised cases where you would, but those would be exceptional. Not the normal "boating lake" or "holiday" scenarios.
The terms have slightly different meaning, but in the areas in which they overlap they are generally interchangeable. understanding the difference in meaning - including where they don't overlap - will help you to understand when you can swap them.
Hire is a very straightforward term to understand. It means to gain temporary use of something, or temporary use of their skills etc, in exchange for payment. Sometimes it overlaps with rent where it means taking possession of some physical thing - you can rent a car, or hire it, and it means the same thing. Which is preferred probably depends on dialect. The same principle applies to hiring a person, meaning taking them into your employment or securing their services as a contractor. You pay them, and for a limited time (or for a specific task) you get the use of their time, skills, knowledge etc.
Take on is a phrasal verb meaning a range of things, but all amount to a sense of something become part of, or an attribute of, or residing on or inside another thing. So a ship "takes on cargo" in port, or indeed it might "take on supplies" as well. Someone trying to disguise themselves "takes on a new appearance". Someone who agrees to be responsible for something "takes on responsibility", and someone who agrees to do a task "takes on a task". It is in the same vein that we use "take on" to refer to someone being hired by an employer - they are becoming part of that organisation. By extension of that, we also use "take on" sometimes for contractors, even when they aren't becoming part of the organisation at all.
So, in your examples, it's fine. But don't assume it will be fine everywhere.