Let's see.
1. HR happened.
2. HR cleared the CF batter's eye.
3. There is a road and a parking lot directly between the stadium and the river.
4. Is there driftwood in the Ohio River?
I'm going to chalk this one up as PLAUSIBLE.
No, there are actual reports and "stories." The stories are fun and cute. The actual reports show that Mantle only faced him 19 times and k'd 12 times. The game logs are available for you.
https://sabr.org/bioproj/person/dick-radatz/
Over his first three years, the Yankees’ Mickey Mantle had only one hit against Radatz. It was a home run. There was a story that circulated in later years, printed in a number of publications, that Mantle had faced Radatz 63 times and struck out 47 times. Asked by this author to run the actual totals back in September 2002, Dave Smith of Retrosheet found that Mantle had 16 at-bats against Radatz and struck out 12 times.