Compliance with WLAN and Bluetooth product standards are not part of CE/FCC/IC compliance. The latter are only concerned with radio immunity/emissions and not about product conformance to industry standards.
Tests against product standards are probably already carried out by whoever made the radio module, and if you haven't changed anything there, you shouldn't need to carry out new product tests. Meaning: be careful with which antennas that are used and only use those that have been used in product testing.
Tests against CE or FCC or IC is something else. For example for CE marking, you need to test against EN/ETSI 300 328, which only cares about the radio being a 2.4GHz wideband "thing", be it Wi-Fi or Bluetooth. The nice thing here is that if your product has Wi-Fi and Bluetooth active at the same time, you get both tested under the same standard, given that they both use 2.4GHz.
If you can ensure that the Wi-Fi radio is electrically disabled and will never be active, then you shouldn't need to test it. That is, if you can ensure that it never emits a carrier wave and never acts as a receiver. In that case it can be regarded as a 'chunk of electronics' and will be covered by the immunity/emission tests of the rest of the product.