If at all possible, I'd try to test the pens on wood that is finished the same way as your sign (perhaps on the back, if it's finished). Depending on how/if the wood is sealed, the type of stain, etc., it can have a huge impact on the way it takes ink/paint. We took daughter's to Michaels (they typically have tons of pens in a big open display) and tested a bunch of them to find an ink that didn't bleed, the right degree of fineness for the tip (not too thick, not too thin), and test color options. Daughter was surprised to find that what she thought she wanted wasn't her best option. Good luck!
I would definitely test the markers on the back of the sign. My sister had a wooden guest book and I'm not sure what brand of pens she used but they smudged all over from people putting their hands on the wood while they signed. I am just going to use normal black sharpie because they dry fast and won't smudge. Then I will put a sealant on the sign with the signatures.