I was going to suggest a spray route previously, but only if you have access to spray equipment.
There's a simpler option you might like to experiment with and it uses nothing more sophisticated than watered-down white emulsion, although any paint suitably thinned would work similarly. Ease of application will vary depending on what you use but this is achievable using a wide variety of paints.
Depending on the wood you plan to use a somewhat similar look is possible through bleaching, using two-part wood bleach.