No, Wii Points can't be converted for use in the Nintendo eShop. They can only be used in the Wii Shop Channel on the Wii console they were redeemed on.
The Nintendo Points currency system is not supported by the Nintendo eShop, currently available on the Nintendo 3DS and Wii U, as well as future Nintendo consoles, and will eventually become fully obsolete on the Wii and Nintendo DSi as well when Nintendo's real currency-based system becomes standard. In Japan, the Wii and Nintendo DSi shops already converted to the new currency system that is used by the Nintendo eShop. In the case of Wii U, however, it currently provides legacy support for Nintendo Points via Wii Mode, which allows access to the original Wii Shop Channel.