Your question implies that having a radar reflecting hat is somehow going to prevent you getting hit by a large ship that is using radar. This is at best wishful thinking.
In most cases human powered boats have the right of way, except in narrow channels.
A vessel of less than 20 meters in length or a sailing vessel shall not impede the passage of a vessel which can safely navigate only within a narrow channel or fairway.
A vessel shall not cross a narrow passage or fairway if such crossing impedes the passage of a vessel which can safely navigate only within such channel or fairway. The latter vessel may use the sound signal prescribed in Rule 34(d) if in doubt as to the intention of the crossing vessel Source
If the large/fast vehicle is not able to visually see you, the radar hat is not likely to make a difference. While not real, this YouTube video Navy Ship vs. Lighthouse provides an insight into the mind of the operators of large vessels. The ships/boats using radar are using it to protect themselves from running into something harmful to them.
If you are in a narrow channel or shipping lane, they have the right of way; you need to keep out of their way. If in the open ocean, they are not expecting anything tiny that needs to be avoided; you need to practice defensive boating. Kayak like you are invisible, because... well, you are.
The graph in the question is about being visible to a ship at ⅛ to ½ mile; the person in the kayak can see the ship at 2+ miles away.
Sitting in a kayak: The distance to the horizon for someone sitting in a kayak is approximately 2.1 miles. When you’re sitting in a kayak your eyes are about 2.5 feet above the surface of the sea–this is why waves appears so big when you’re in your kayak. 7 x 2.5 = 17.5 and 17.5 / 4 = 4.375 and sqrt of 4.375 = 2.09165. Source
The kayak is significantly more maneuverable than a large ship, the kayak can see the ship sooner and get out of its way, and is the only vessel at any risk in a collision. The kayak is not allowed to cross a shipping channel if they are not able get out of the way ("shall not impede the passage"). In the open ocean, a kayak theoretically has the right of way, but realistically there is no point in being "dead right".