You're saying that they don't have much technology, that can suggest that the setting was around the Middle Ages. The fact that it is a heavy fortified city also points in that direction, so I'm gonna focus my answer on that time.
You say that you can walk from one side to the other side of the city in about two minutes. Given that you walk 5km/h that would give you around 133 meters. Assuming that the city-fortress is square, that gives you 133^2 = 17,689 square meters. In that small area would live around 250 people if the population density would be the same as in the center of Amsterdam. The density in the middle ages would be different I guess, but I couldn't find any information about population density in cities in the Middle Ages, sorry ;-). This gives you enough people to create a small society that could survive on it's own.
What they should do first is to create a food industry that produces more than enough for all of them, if they didn't already have that. This is necessary because they can't go to another city that easy if they run out of food in the middle of the winter, and they don't have allies any more which will help them in problems. In the case of urgent clothing need, people could go hunt and make clothes from animal skins. Maybe they don't have that technology yet, but it isn't hard to acquire.
If they can support all necessary elements for survival themselves they can look into creating valuable goods that other cities and villages in the area want. The tricky part is what. They have skills in metalworking and woodworking, but only have access to wood (the question is also about how they would get ore, so I'm assuming they don't have access to that). And I don't think the cities and villages in the neighborhood would have much trouble to acquire wood too. I think they have a couple possibilities which are rather easy to realize:
- Focus on increasing their agricultural output and sell the surplus.
- Focus on hunting and sell the skins.
- Focus on cutting wood and crafting furniture and building materials and selling those (although I'm not sure if there will be a big market for it in the situation that the area is currently in).
They should try trading with cities and villages which have the ore they need to create metal tools and other objects. As soon as they can establish a continuing trade with such a city/village they can keep buying ore, turning it into valuable tools and other objects and sell it for more. If they acquire enough skill in metalworking they can become a trade-hub in the area.
So my final answer would be: Yes, they can get enough necessary supplies through merchants.
This is of course a best case scenario, many things could go wrong or make it harder, I'll name a few:
- New wars could break out
- All cities and villages in the area are wiped out and you need to travel for days or weeks to get to the closest one.
- Cities and villages in the area doesn't need your stuff because they can provide for themselves.
Because the question left much to the imagination this can be the answer you're not looking for. If not, specify your question a little better please. Think about the following aspects:
- What year/era this is happening
- Peaceful or dangerous area
- Are the other cities and villages close or not
- In which area is the city located, desert, mountains, forests, fields, ...
- What climate does the city have, around the equator, close to the arctic, ...