On the whole, there’s nothing in what Stephen Hawking is reported to have said at a recent lecture that is incompatible with theism broadly or Catholicism specifically. Human beings are part of nature, and our actions affect the course of the universe to some extent. Theologically, we are called to make of ourselves God’s instruments (although I’d propose that the higher benefit comes spiritually, with the fact of our having done the act, rather than materially, in the task that we accomplish).
There is a certain danger lingering behind such thinking, and it’s one that justifies admonishments against “playing God.” Humankind has a way of backing into pits as it seeks to skirt obvious falls. Consider even just the last two paragraphs of the above-linked post:

But we are now entering a new phase, of what Hawking calls “self designed evolution,” in which we will be able to change and improve our DNA. “At first,” he continues “these changes will be confined to the repair of genetic defects, like cystic fibrosis, and muscular dystrophy. These are controlled by single genes, and so are fairly easy to identify, and correct. Other qualities, such as intelligence, are probably controlled by a large number of genes. It will be much more difficult to find them, and work out the relations between them. Nevertheless, I am sure that during the next century, people will discover how to modify both intelligence, and instincts like aggression.”
If the human race manages to redesign itself, to reduce or eliminate the risk of self-destruction, we will probably reach out to the stars and colonize other planets. But this will be done, Hawking believes, with intelligent machines based on mechanical and electronic components, rather than macromolecules, which could eventually replace DNA based life, just as DNA may have replaced an earlier form of life.

I’m inclined to assert that voluntary elimination of such traits as aggression is utterly impossible, even if it becomes technologically plausible. At some point, people who refuse to submit will have to be forced or pushed off the evolutionary cliff (by sterilization or incarceration), otherwise they’ll return to rule their passive brethren. Then, there’s the possibility that removing aggression will derail technological advancement or that humanity (or its post-human surrogates) will encounter something in the universe — another alien species, perhaps — that requires an aggressive reaction.
More basically, though, there’s an ontological difficulty in the second paragraph of the block quote: We begin with the prospect of removing our capacity for self-destruction only to end with the creation of life forms that would replace us! Clearly, prior to any decisions about our self-directed evolution must come a conclusion — an unlikely consensus — about the source of value in the universe. Adherents to scientism assume that value, leaving it deliberately unstated, and to the extent that they are not entirely oblivious to the fact that they have done so, they rely upon a sort of intellectual conceit that they know better… or at least that the process of thinking to which they adhere necessarily points in the direction of Good.
Ultimately, their imposition of a preferred evolution of mankind will come down to raw power, and one way or another, those qualities of human nature with which many of us have discomfort will be written into our program for the rest of our part in the universe’s history, if only because it is also written into nature.
(I spent a fair amount of time with my head in these clouds a half-decade ago, if anybody’s interested in more.)