Back then the US had no trade agreements, belonged to no international trade organizations and did whatever we want to do, acting unilaterally when, where and how we wanted to. No country or international tribunal told the US what to do with its trade rules (though they could and did retaliate when we did something they did not like, such as raising tariffs).

Then FDR came along and 'messed things up' - from a Trump perspective - and had the idea of countries governing trade cooperatively rather than each one going for maximum advantage to the detriment of all the others.

I think Donald would love to tear up existing agreements (he is an authoritarian who will act 'decisively' after all) - which he would have to do to unilaterally impose tariffs on Mexico, China and other countries he does not like. If he negotiated new trade agreements at all, which I doubt, they would be only bilateral with the US always the stronger and bigger partner so that we could impose our will on the weaker, smaller 'partner'. And you are right, his corporate buddies would do the negotiating, not labor unions or environmental groups whom he undermines at every turn.

making new ones.

I think he prefers to act unilaterally rather than negotiate new agreements that would limit him later. That is what Coolidge and Hoover did and he seems to be a throw-back to the republicans of that era. They raised tariffs to protect the domestic market of the corporations who provided their campaign funds. It seems that corporations exert their influence no matter what the policy is.

I'm sure if Trump did negotiate new trade agreements, it would be his corporate buddies doing the negotiating. If he decides to raise tariffs unilaterally instead, his corporate buddies will probably negotiate those details as well.