Is tracheotomy safe for a cancer patient having breathing problems?

Yes: Tracheostomy is usually needed for obstructive problems of the airway or prolonged respiratory failure requiring ventilation not usually isn't a good situation.

Some risk: It may be the only way to save the life. No operation is without risk, benefit, options to be discussed.

Overall yes: If it is something that is planned and elective as opposed to emergent it is very safe with relatively few risks or complications. Risks and benefits must always be discussed and weighed with your medical team. If someone is very weak with a very low white blood count or a tendency towards bleeding due to cancer or its treatment, the risks are increased over an otherwise well person.