For easy climbs you have quite a good chance to be OK with hiking shoes.
The most important property for a shoe to be usable for climbing is, that you have to be able to stand on contact points so small that only a part of your toes' length fits on them. To achieve that, you have basically two possibilities:
- You take a flexible, very tightly fitting shoe with a thin rubber sole where you can stand on small pieces by actively exerting force with your toes and the arch of the foot. This is the climbing shoe approach.
- Take a quite heavy shoe with a sole that is stiff enough that it does not flex when you stand on a small edge at the very tip of the shoe. In that case the force to stand on small items comes from your ankles. Hiking boots which are at least partially crampon compatible typically have such stiff soles. Also, this type of shoe was the normal climbing shoe before the invention of specific rock climbing shoes. Of course you will not be able to stand on super-tiny edges and your mileage may vary depending on the type of rock but for easier climbs and the occasional climbing or scrambling section on a hiking tour you will be quite fine.
Both shoe types have in common that their sole has a pronounced rectangular front edge which allows to step on rather small edges with good precision.
Other types of shoes, such as trainers or gym shoes will be much worse compared to those, since they have a thick, but very flexible sole (causing not very precise feeling for the things you stand on) and if chosen at a wearable size are reaching too much over the front of your toes, such that you have neither have a defined front edge to stand on nor a good force transmission to the sole, so it will be very strenuous for the toes and arch of the foot muscles to stand on small features.
To summarize: if you want to take it serious and can afford the extra money, pack weight and space, go for real climbing shoes. For easy climbing or some occasional climbing section on your hike, your hiking shoes should do OK. Normal sports shoes will perform much worse, so taking those will be a waste in money and energy -- the latter both while carrying them and while climbing with them.