No companies that manufacture routers appear to offer personalized casing to this degree. However, it is possible to have custom exterior casings produced for anything through a personalized crafts site, such as Etsy.com. Factors such as the dimensions, antennae, Ethernet and power ports would need to be taken into account.
A brief online search does not reveal any specific companies that make designer Internet router exteriors, however there is no clear technical reason why wood would be unsuitable as a casing material. Wood is not electrically conductive and so should not significantly weaken a wireless router signal. However, it is important to avoid use of nails or conductive metal in the construction, as these materials can weaken or block the wireless signal.