Do I need to replace water damage or just let it dry out?
Jeremy, I would strongly suggest you use a Multimeter to measure the water content in your wood flooring, and other materials around the sink.  Please view this link to a suggested meter you can purchase,  it has prongs so that you may penetrate into the wood with minimum damage and get a reading from the inside, as water can stay contained withing the wood.  If the leak was dried within 48 hours and you have a water content less than 16% on your wood and other damaged materials, then you should be safe. If the leak was not dried withing 48 hours, or the water content in the wood is higher than 16%, I would strongly suggest you hire a air quality inspector, he can take a sample from your kitchen air, and tell you if you have elevated amounts of spores indoors, and if you have mold species that can affect your health.  I would make it a priority to ensure moisture is not higher than 60% throughout the house as this can trigger mold to grow.  Some species are known to stay dormant for 48 hours and sprout airborne, which can cause further damage to the A/C system.
Also if you have access to a FLIR infrared camera, this can help you detect if there is moisture in the drywall, or wood frame behind the sink.
It is true that mold is in every environment but elevated amounts of certain species such as aspergillus penicillium, or stachybotrys can cause allergies or infections to your respiratory system.
I am a professional mold remediator, hope my advice is of help.