- Addie Joss, 4/20/1910, CLE 1, CHW 0; 5th game
- Rube Marquard, 4/15/1915, NYG 2, BRO 0; 2nd game
- Eddie Cicotte, 4/14/1917, CHW 11, SLA 0; 3rd game
- George Mogridge, 4/24/1917, NYY 2, BOS 1; 9th game
- Bob Feller, 4/16/1940, CLE 1, CHW 0; 1st game
- Tex Carleton, 4/30/1940, BRO 3, CIN 0; 9th game
- Jim Tobin, 4/27/1944, BSN 2, BRO 0; 8th game
- Ed Head, 4/23/1946, BRO 5, BSN 0; 7th game
- Bob Feller, 4/30/1946, CLE 1, NYY 0; 10th game

The Wikipedia page has that information.

"While the vast majority of no-hitters are shutouts, no-hit teams have managed to score runs in their respective games a number of times, but only twice has a team been no-hit and still won the game. The Cincinnati Reds defeated the Houston Colt .45s (now called the Houston Astros) 1-0 on April 23, 1964, even though they were no-hit by Houston starter Ken Johnson, and the Detroit Tigers defeated the Baltimore Orioles 2-1 on April 30, 1967, even though they were no-hit by Baltimore starter Steve Barber and reliever Stu Miller." (Emphasis added.) Your question seems to ask how many starting pitchers were charged with the loss in no-hit games; Johnson and Barber did take the losses in these games.

Games classified as no-hitters before 1991 include a) no-hit games pitched by visiting teams in which the home team led after the top of the ninth (4, including the Andy Hawkins 0-to-4 and Matt Young 1-to-2 games), b) shortened games (1 loss, in the 1884 Union Association), and c) no-hit games broken up in extra innings (11 losses, of which one was debited to a relief pitcher).

So the broadest answer to your question appears to be 18, with the qualifiers that 16 of those games do not meet the formal present-day definition of a no-hitter. The loss in one of the "non-qualifying" no-hitters was charged to a relief pitcher who pitched only one inning. Eleven of the 18 games went into extra innings, during which the team hitless in regulation got at least one base hit and won the game. Mr. Haddix could quibble, but those aren't really no-hitters. One no-hit loss lasted five innings and took place in a marginal major league in an era when the lone umpire wore a top hat — again, probably not a real no-hitter. The other six no-hit losses were completed in nine innings, although four of the six were pitched by road teams who didn't have to pitch the bottom of the ninth, thus disqualifying those games from the formal present-day definition of a no-hitter. Per the paragraph above, the narrowest answer to your question is two.

I love how in some of the early no-hitters the team with no hits scored two runs. Although it wasn't until 1967 that a team with no hits and two runs actually won the game.

List of MLB no-hitters

List of MLB perfect games

A quick search using PI team game finder yields 153 no-hit games (1920-1939, 1952-present) of 9 innings or more, and only 12 had no base runners. So it looks like 1 in 12.75 or slightly less than 8% of no-hitters are perfect games.

Eighteen of 263 = 6.8%.