As many as 118 Test players played in 5 or more matches and never saw a draw. These are the top few:
This list is headed by a current player Aiden Markram:
Next is the 19th-century player GA Lohmann (18), England’s leading pace bowler of that time.
Then there is the near-current player KK Jennings (17) who has some chance of playing again, along with Alok Kapali with his record 17 losses. Baptiste with his 10 wins is further down.
From India there is a current player HH Pandya (11).
Other current players include SO Hetmyer (16), Hasan Ali (13), KM Jarvis (13) and TA Blundell (10).
Of course, Markram will lose his status once he plays in a drawn Test, which means that the record will go back to the venerable George Lohmann.
South Africa last had a draw in March 2017. This was followed by 34 Tests with results. Thus a number of junior Test players from there have 5 or more Tests without a draw. This applies to most of the current team.