By the time Hawkeye and Hank Pym were teammates, Hank was no longer Ant-Man, and thus Hank as Ant-Man and Hawkeye only were in the same issue a couple of times, and in one of those instances, Ant-Man was fighting the Avengers. So the first time Hawkeye was even really given the chance to do the trick was with the new Ant-Man, Scott Lang, so that 1982 Avengers #223 would be the first time they did the trick.
Atom and Green Arrow were teammates for a long time, and honestly, who knows, maybe they did the trick many times earlier. I really don't know, as the question here was just "Who did it first?" So when I found that answer, I just stopped looking.
Here, from 1976's Brave and the Bold #130 (by Bob Haney and Jim Aparo), Atom and Green Arrow team-up to rescue Batman from a death trap...
My buddy Xum also noted that in 1973's Justice League of America #105 (by Len Wein and Dicks Dillin and Giordano), Arrow and Atom pulled the trick off, as well...
If anyone else sees an even earlier one, I'll also add it in for fun. But this is just for fun, as the main question is just "Who did it first?" And that's answered already. But, again, I'll gladly add in earlier examples of Atom/Green Arrow pulling the trick off.
Reader Joe came up with a fascinating point. While Hawkeye never fired Hank Pym on an arrow as ANT-MAN, he DID do it with Hank as a shrunken down Goliath in 1968's Avengers Annual #2 (by Roy Thomas, Don Heck, Werner Roth and Vince Colletta)
I figure that's close enough that we SHOULD count that, right?
Greg Geren settled the matter pretty definitively, though, when he noted that Atom rides one of Green Arrow's arrows in Justice League of America #22 (by Gardner Fox, Mike Sekowsky and Bernard Sachs), which was released in 1963, a year before Hawkeye was even INTRODUCED!
So that settles that. So there ya go, Gareth! Coincidentally enough, that was the answer Gareth was hoping for, so even better.
If anyone else has a comic book question that they'd like to see answered, feel free to drop me a line at firstname.lastname@example.org!