Marshall gambit? Even experts have difficulty learning that stuff. I suggest Open Sicilian Shveshnikov.
what is the most drawish opening?

When supported by his thousands of other games, the conclusion is obvious: he doesn't draw games, shouldn't attempt to draw games and should focus on improving his play and playing the best moves instead.
19 is enough anyway, find me a GM without a draw in their last 19 games.
I disagree

Persuasive.
Well If your talking to me I will say. I wasn't trying to be persuasive. I just simply disagree because I saw what you said as well as other's and thought about it and realized. The OP is doing something good.
Line's which give high draw rates are considered very solid line's. They are so solid that both sides usually find resources to stop/prevent others from having any successful attack which is why the games end up in a draw with high draw percentage rates.
As you have stated the OP has a very low draw percentage. Which means if his drawing percentage is very low the outcomes of his games are either wins or losses.
Considering his ranking is not extremely high. It is safe to assume we know the outcome of the results has been leaning more to losses.
Which means he is doing something wrong. He realizes he is doing something wrong and is trying to find a line with better drawing percentage. Which means he is looking for a more solid opening which is capable of giving better drawing chances. He realizes a draw is better than a loss and their is no shame in drawing.
Something which is very hard for beginners to understand. It can take years for a beginner to realize you can't win every time sometimes all you can strive for is a draw especially with the black piece's.
My advice for the OP is a recommendation of a few line's as well as to say keep up the good work.
With the White piece's some very solid line's which are recommended to beginners are:
Italian Game
London System
Though they are recommended to beginners becuase they have short opening theory even high level players can play these line's. Many high GM level players simply don't play them not because they are not solid but becuase of their high draw rate. Which is a good thing. If it has a high draw rate it means its solid.
I play both line's even today. They give good piece play and are solid positions are usually equal but at least you don't have to worry as much of falling into any opening traps.
As for playing with the black piece's the most Classical way of playing is simply responding with a pawn in the center for example.
1.e4 e5 as black
1.d4 d5 as black
Those are the most classical way for black and are considered solid;however, their are also other lines which can be played which are solid. The draw back is they require some theory or opening knowledge. Some lines are sharper than other's.

Here are some drawish openings.
English 1. c4 40% draws
4 Knights 1. e4 e5 2. Nf3 Nc6 3. Nc3 Nf6 40% draws
French Defense Tarrash 1. e4 e6 2. d5 d5 3. Nd2 40% draws
And now the winner for the most drawish chess opening....
French Defense Exchange Variation 1. e4 e6 2. d4 d5 3. exd5 42% draws

More than one third of games in Capablanca´s Variation of the Caro-Kann Defence are drawn.
Actually, after the very common order of moves, 1. e4 c6 2. d4 d5 3. Nc3 dxe4 4. Nxe4 Bf5 5. Ng3 Bg6, 42% of games are drawn, according to a 7.5 million database. In adittion, I read a couple years ago, that when Petrosian wanted to draw or at least, not to lose haha, he used Caro-Kann.

Petroff is quite drawish IMHO.
It's Pretov's defense, and yes, that was gonna be my choice also.

Marshall gambit.
Advice? Memorize the theory :p
Look at his rating. Be serious.
I figured he had enough serious responses already.
I assume half (or so) say this is the wrong question, you should focus instead on learning all the basics... which is what I would say if I were going to respond seriously.
As for his question "how to do it" if you want a draw, play incisively for the win and keep and active position. When you have a small solid advantage this is when you can consider your drawing options. To draw against stronger players an advantage is all but necessary (because you will make small errors). GMs are different, they have massive amounts of technique and theory to lean on, so they can actually play for a draw from move one.
When weak players "play for a draw" they usually mean they're playing passively. Against a reasonable player this will present you with huge technical problems even if the position is theoretically dead equal.

Petrov Defence (Russian game) is the most drawish. After 1.e4,...e5, 2.Nf3 Black just plays ... Nf6 and most of games, especially, if it's Queens exchange, are drawish. But in my opinion, 2...Nc6 is better move

Ok. Ruy Lopez, Berlin defence, open variation is very drawish. It is aggressive opening, and it is drawish, if Queens are exchanged. Only drawish for top players too?

"How good is the karo cann?"
Very good. When playing for a win, I occasionally play that. The advance variation is a little cramped but it is very good strike at center for black early on.

mere assertion