Nobody is going to stop trading with us. Nobody is going to stop buying / selling products to or from us...
It's the renegotiation of deals at a national or business to business level (as a result of national deals) that change the terms. To you and me that's the cost of products and services.
I don't think a single person on either side of the camp has suggested we will cease trading with certain other nations, that's not even up for debate. The debate is the effect of being in or out on those trade deals and what it means for both large and small businesses - which ultimately means prices / jobs to the UK population.
If we leave the EU, we will badly wound it. That's not necessarily a victory to celebrate - we still have to take care of ourselves outside the EU. However, as a wounded animal, the very least we can expect is some animosity.
Some people we will have an elevated level of power over the EU, others believe otherwise. We will just have to wait and see how that pans out. But I really cannot the EU rolling over and having it's belly tickled after being wounded (even if it's the right move to leave).
We can argue until the cows come home about who needs who the most... it doesn't mean either side will make purely logical decisions.