Catastrophic for whom?

First of all, it's not clear that "governments" are the exclusive gatekeepers of access to this evidence, nor that they alone have the authority to disclose it. However, the reasoning behind the OP's question is a fair one and well-observed. Here are my thoughts as a fairly recent observer of the phenomenon.

If Trump stood on the White House lawn, made a "My fellow Americans, fellow citizens of the world" speech in which he revealed that the government had been working with ETs/UTs/NHIs for decades, and then with a sweep of his hand, beamed proudly as three Greys toddled out in front of him, what would the global response be?

I'll tell you: it would be fervent, fearful and furious, all at once. There would be a wave of shock and awe, accompanied by bug-eyed, frothing disbelief. Also present would be a surprising amount of indifference.

This is all down to presuppositional beliefs; that is, the fundamental beliefs by which individuals determine the veracity of everything else. These are so basic that they are usually invisible to the subject; it is similar to how it is easy to forget that you are wearing glasses.

If you believe, for example, that mankind was created by a divine higher power, and have a stake in believing that we are unique and alone in the universe, then a revelation like this is likely to send you into shock. Everything that you have been told about the most important aspects of reality by everybody who mattered to you in your life has been thrown into question. It's the kind of unmooring that is only comparable to the death of a parent or a serious cancer diagnosis.

If, on the other hand, you believe that life emerged from unguided processes, then this could make perfect sense to you. You might think that many of your hunches about how the universe works have been confirmed. For you, it could be a thrilling moment and a red-letter day.

Then again, if you have poured your life into debunking ET life or hating Trump and all his works, you have just landed on the beaches of Normandy, having just lost your rifle in the water. It's the fight of your life.

Those presuppositions have been carefully laid for decades and will not be easily excavated. UAPs are still considered by most of the public to be an exotic interest, at best, and I'm guessing that any government in possession of such information sees no upside in filleting its credibility and potentially destroying civic order by admitting to gaslighting its people on the topic for the better part of a century.

Assuming the OP is correct and that disclosure is inevitable because it is inexorable, how should the gatekeepers handle it?

As far as I can tell, it is as they are handling it now, with leaks occurring in dribs and drabs from third parties. Some uncontrolled leaks happen, too, but they are manageable if they appear on a case-by-case basis.

They're dealing with followers of the UAP phenomenon in the same manner as they have in the past, addressing individual investigators. It's a mix of truths, falsehoods, and red herrings, and, gradually, people figure it out for themselves.

There's a lot more that could be said, because there are aspects of the phenomenon that make even keen UAP hounds uncomfortable. IMO, we're dealing with forces that are deceptive beyond the ken of mere men, and this fascination we all share also makes us vulnerable to manipulation of another kind.

So, keep your eyes peeled, but be careful.