Salamun Alaikum
The only prohibition on a believer is the consumption of non-halal food items.
As an example, in my humble opinion a good judgment call would be not to trade in these goods if it is your business and where you exercise control over what you sell and what you don't. If for example you are working in a supermarket whose main business is not selling liquor then I would see no problem working there either.
However, working in an off-licence or 'bar' would be against the spirit of the message in my humble opinion. If you only dealt with pork items for public consumption, then again, this would also be much akin to the off-licence example and not in the spirit of Islam.
Similarly, in a culinary school, your main purpose is not to consume or sell a particular commodity. You are there to learn to cook. As long as you don't consume it for yourself, I don't see much of a problem.
However, I would add that in a ‘learning to cook’ process, I am assuming one is required to ‘taste’ the food in some capacity? Again, if there are any non-halal food items, then this would become an issue. So sensible judgment calls need to be exercised and in my opinion, it is best to see if you can avoid the situation completely.
At the end of the day, a lot of teaching institutions / people are accommodating. It’s a case of just asking and discussing your reservations.
I always feel it wise to err on the side of caution when one feels they have a judgment call such as this to make. But inherently, there is nothing wrong in touching / handling as long as it is not for sale as a main item of your business or for consumption.
Regards,
Joseph.