Players who have made only a single league appearance for United in the last 30 seasons (those in bold have played other games in cups):
Nathan Peel 1991-2 v Tottenham (sub)
Mervyn Day 1991-2 v Wimbledon
Carl Muggleton 1995-6 v Reading (sub)
John Ebbrell 1996-7 v Reading
Chris Bettney 1996-7 v Tranmere (sub)
Brian Launders 1999-2000 v Stockport
Manu Thetis 2000-1 v Gillingham (sub)
Ryan Mallon 2001-2 v Grimsby (sub)
Lewis Killeen 2001-2 v Walsall (sub)
Richard Edghill 2002-3 v Ipswich (sub)
Gary Kelly 2002-3 v Watford
Lee Baxter 2003-4 v Burnley
Phil Barnes 2004-5 v Rotherham
Tommy Johnson 2004-5 v Rotherham
Emmanuel Gabrieli 2004-5 v Gillingham (sub)
Danny Batth 2010-11 v Swansea (sub)
Graham Kelly 2015-16 v Coventry (sub)
Nathan Thomas 2017-18 v Norwich (sub)
Regan Slater 2017-18 v Preston (sub)
Jake Eastwood 2017-18 v Wolves (sub)
Ravel Morrison 2019-20 v Leicester (sub)
Jack Rodwell 2019-20 v Burnley (sub)
Rhian Brewster 2020-21 v Fulham (sub)
Max Lowe 2020-21 v Fulham
Some of these players will likely fall off this list at some point (perhaps as soon as this saturday for Lowe and Brewster).
I think Killeen, Mallon, Baxter and Graham Kelly are the only ones not to have made a PL or football league appearance for any other team.