Noah's suggestion to use "blue" shampoo might help. But before you decide you really need to better understand color and color issues as it relates to hair. I am a professional artist and colorist (not coloiist as it apples to the color specialists often found in hair salons.). I work with traditional paint and brushes and I work digitally creating imagery regularly for designers......commercial and residential. ....worldwide as well as art consultants, galleries, etc. I typically have to mix to colors to exact specifications based on a designer's color scheme. Color mixing is a science.
Back to blue shampoo. The reason one often sees the recommendation of" blue" shampoo is because human hair hair pieces eventually become brassy. Brassy by definition has a strong orange component. Orange is created by mixing red and yellow. On a color wheel, if an artist wants to neutralize a color (desaturate, reduce chroma) the artist selects the color opposite, 180 degrees, on the color wheel. Opposite orange is blue. Thus the blue shampoo recommendation. The OP of this thread states he has "red" hairs. Opposite red on a color wheel is green. Thus the OP might want to consider "green" shampoo.
Do a Google search for blue shampoo and for green shampoo. Lots of links and some very interesting reading.
I came across this link.
http://www.theperfumeexpert.com/how-to-fix-brassy-hair-and-remove-other-unwanted-red-tones/
Well written, and, from a color theory perspective very accurate. The writer wants to sell an ebook. But she presents great information on this link for free. It is a good read. There is also a color wheel on the link. Checkout red and orange and their corresponding complements.....180 degree opposites.
Also read user comments below the link As expected a mix of responses. Nothing unusual about that. This forum, particularly the "baldness is death side" with all the solutions, magical treatments, drugs, cures, etc is filled with some quite nasty confrontations and disagreements. It is the internet. To be expected.
When I mix color for my bio hair sides and back, or if I am correcting hair color on a hair piece (human not synthetic) I use a mix of dark ash, dark brunette and a touch of black usually with 20 developer or 30 developer. Never 40. The brunette darkens the ash. But it also adds a slight red cast. A very small touch of black desaturates the red cast.. This is not a process for the beginner. But if anyone on this forum is having similar issues with color either on their bio hair or their hair piece that has now changed color (brassy or otherwise) I am willing to provide suggestions and caveats.
To the OP. In your post you do not detail the frequency of the red hairs. Many or only a few? Also what kind of light are you using to view the color? Light source makes a huge difference. I paint with 5500 Kelvin lighting because it is color neutral. Professionals in all fields when evaluating color typically use "viewing booths "that are color neutral. When working digitally I use a colorimeter to profile my monitor so that it accurately depicts color. The point I am making is color is complicated! Everyone's hair piece changes color appearance with light.......sun, shadow, blue sky, halogen, florescent etc. Produce different color perceptions.
If you only have a few red hairs I would remove them manually rather than get into all these color issues. Tweezers work. I prefer a German ventilating needle with needle holder. The needle easily slides into the knot facilitating easy loosening and removal. Less chance of lace damage.