There are no official records for actual on-air contacts that I know if and it would be extremely difficult to establish them because (unlike at HST competitions where a team of judges is watching the competitor) it's impossible to detect cheating and there are no clear rules how to measure the speed.
There are some clubs dedicated to high speed CW operating without keyboards, namely the High Speed Club (HSC), Very High Speed Club (VHSC), Super High Speed Club (SHSC) and finally the Extremely High Speed Club (EHSC). The conditions to join these clubs are to receive a recommendation from existing members for Morse contacts without the help of decoders or encoders (other than standard keyers) at speeds of 25 wpm, 40 wpm, 50 wpm and 60 wpm respectively (125, 200, 250 and 300 characters per minute).
While the "basic" HSC speed of 25 wpm is something that many hams can easily achieve, at 40 wpm the air is getting quite thin: The VHSC has 421 members, SHSC 186 and EHSC 114.
So there are some hams on the air who can send and receive at 60 wpm (at these speeds, the sending is the limiting factor for most operators - there are numerous hams who have shown that they can do head-copy at speeds of up to 100 wpm!) with a paddle (no keyboard).
Why is the official Guinness record (as cited in another answer, 216 letters per minute by Andrei Bindasov) so much lower than 60 wpm?
Two major differences:
- Those 216 letters were real sent characters, not measured by the PARIS standard. When you use completely random letters (the record was done at a HST championship with random 5 letter groups), 216 letters real are approximately 260 characters according to PARIS (52 wpm) due to the different distribution of character lengths.
- At the HST competition you have to transmit one minute of random 5 letter groups from a sheet of paper you have never seen before, which is more difficult than sending plain text in a language of your choice. If you make an error and have to repeat a group, the repetition of the wrong group does not count as additional sent letters.
In on-air contacts you may make mistakes which you don't even bother to correct, because an extra dit here or there will not make a difference for the receiving party. So comparing on-air contacts with HST competitions is comparing apples and oranges.
Bottom line: Amateur radio Morse code contacts with manual keyers (not keyboards) at around 60 wpm are well documented.