user5784: Which player of the top 50 has the lowest drawing rate ? Who is it in the top 100 ?
And which woman in the top 50 has the lowest drawing rate ?

user11133: Without controlling for strength and for strength of opposition the above is largely meaningless--no offense intended. You would expect Bobby Fischer to play fewer draws, for example, simply because he so thoroughly outclassed nearly all his opposition. 
That does not mean, however, he was not predisposed to drawing. It means that he didn't play enough players of his caliber for us to know his tendencies. 
The converse is true--take a weak player who likes playing over his head. He won't draw often, but that does not mean he is not predisposed to drawing.
You'll have a better chance of generating a meaningful result if you account for strength of opposition, eliminate games played for GMs when their rating was under 2500... perhaps a variable coefficient based on strength of opposition... you get the idea.  

user3872: According to the FIDE statistics, caruana draws 40 percent of the time and nakamura draws 41 percent. Out of top 12 individuals I checked, these are the lowest. Nakamura is famous for not accepting or offering draws but likes to play everything out. 

user3831: Looks like I am late to the party. Anyway:
Free PGNs of many top players are available here. Almost all 2700+ players are there. As for women, only a few from very top are there. These PGN files have anywhere from few hundred to couple thousand games available for each player. Although this does not fully comply with OPs request, it seems like an improvement over the current only answer. If you have some better/more PGNs available, you can post a download link in a comment or run them through this script and suggest an edit to this answer.
The results


EDIT
Bonus - world champions.

Also of interest - Morphy and Anderssen have amazing draw rates of 0.085 and 0.1, respectively.

5784: <p>Which player of the top 50 has the lowest drawing rate ? Who is it in the top 100 ?</p>

<p>And which woman in the top 50 has the lowest drawing rate ?</p>
 11133: <p>Without controlling for strength and for strength of opposition the above is largely meaningless--no offense intended. You would expect Bobby Fischer to play fewer draws, for example, simply because he so thoroughly outclassed nearly all his opposition. </p>

<p>That does not mean, however, he was not predisposed to drawing. It means that he didn't play enough players of his caliber for us to know his tendencies. </p>

<p>The converse is true--take a weak player who likes playing over his head. He won't draw often, but that does not mean he is not predisposed to drawing.</p>

<p>You'll have a better chance of generating a meaningful result if you account for strength of opposition, eliminate games played for GMs when their rating was under 2500... perhaps a variable coefficient based on strength of opposition... you get the idea.  </p>
 3872: <p>According to the FIDE statistics, caruana draws 40 percent of the time and nakamura draws 41 percent. Out of top 12 individuals I checked, these are the lowest. Nakamura is famous for not accepting or offering draws but likes to play everything out. </p>
 3831: <p>Looks like I am late to the party. Anyway:</p>

<p>Free PGNs of many top players are available <a href="http://www.pgnmentor.com/files.html#players" rel="noreferrer">here</a>. Almost all <a href="http://2700chess.com/" rel="noreferrer">2700+ players</a> are there. As for women, only a few from very top are there. These PGN files have anywhere from few hundred to couple thousand games available for each player. Although this does not fully comply with OPs request, it seems like an improvement over the current only answer. If you have some better/more PGNs available, you can post a download link in a comment or run them through <a href="https://gist.github.com/GloriaVictis/18e069d9492f143646c7" rel="noreferrer">this script</a> and suggest an edit to this answer.</p>

<h2>The results</h2>

<p><a href="https://i.stack.imgur.com/kaqZK.png" rel="noreferrer"><img src="https://i.stack.imgur.com/kaqZK.png" alt="draw rates men"></a></p>

<p><a href="https://i.stack.imgur.com/KBmqp.png" rel="noreferrer"><img src="https://i.stack.imgur.com/KBmqp.png" alt="draw rates women"></a></p>

<h2>EDIT</h2>

<p>Bonus - <a href="https://en.wikipedia.org/wiki/World_Chess_Championship#World_champions" rel="noreferrer">world champions</a>.
<a href="https://i.stack.imgur.com/xyjbz.png" rel="noreferrer"><img src="https://i.stack.imgur.com/xyjbz.png" alt="draw rates world champions"></a></p>

<p>Also of interest - Morphy and Anderssen have amazing draw rates of 0.085 and 0.1, respectively.</p>
