I'm sorry, but this entire premise is just ridiculous. The National League is more prone to no hitters because they don't have a designated hitter? LOL, really?
There are 27 outs in a baseball game. Unless the no hitter is also a perfect game, there will be a few more plate appearances for walks, hit batters, hitters reaching on an error, etc. Assume that there are four more plate appearances, maybe slightly more (say three walks and a hit batter). Unless the DH is batting in the top four spots, they're going to get three plate appearances in a game, if that. The Major League average this year is .251. The odds are against the DH getting a hit in those three plate appearances. If a starting pitcher can keep the other eight batters in the lineup from reaching safely via hit, why is it such a stretch to think that they could get the DH, too? A designated hitter is typically an older player that cannot find a position on the field. They're not going to be fleet of foot. So, they're certainly not going to beat out an infield single. They need to get a clean hit off the pitcher, something every other hitter in the lineup has been incapable of doing. And how much of an advantage does the DH provide the American League when a starting pitcher in the National League will usually only bat a couple times in a game? As the game progresses, and a starter approaches their pitch count limit, they'll be pulled, and a pinch hitter will bat in the pitcher's place. That "weakness" in the lineup is only a glaring hole a few times a game.
Did you even bother to look at this year's statistics before starting this topic?
Here are the team by team batting statistics for 2016. The Major League average for runs scored per game is 4.26. Fifteen teams in the Majors are scoring more than the Major League average. Ten of them are from the National League. Eight of the top ten scoring offenses in the Majors right now are in the National League, including six of the top seven. What about pure batting average, since a no hitter is only concerned with hits? Seven of the top ten hitting teams by batting average are in the NL.
What about the DL? American League designated hitters
are hitting a combined .231 this season, twenty points
below the Major League average. They're an improvement over the batting prowess of N.L. pitchers, but on the whole, they are below average American League hitters. Of the fifteen AL teams, only Seattle, Detroit, Minnesota and Boston have DH production above the .251 mark.
Kansas City's designated hitters are batting a combined .213.
Baltimore's designated hitters are batting a combined .210.
New York's designated hitters are batting a combined .200.
Texas' designated hitters are batting a combined .197.
Houston's designated hitters are batting a combined .192.
Los Angeles' designated hitters are batting a combined .188.
Oakland's designated hitters are batting a combined .162.
Tampa Bay's designated hitters are batting a combined .157.
Wow, the American League designated hitter slots are just stocked with great hitters!!
The National League, which you hypothesize is somehow "weakened" by the lack of a Designated Hitter, is kicking the crap out of American League teams, comparatively. Your "hypothesis" is completely unsupportable by the available empirical data.