can i re-use an intel stock cpu fan?

Hello,

I am upgrading my intel build and moving the old components to a secondary pc. I am currently upgrading from an Intel Core i7 3770 to an Intel Core i7 4770k. I have a few questions about this

1. When moving the stock Intel heatsink fan to my secondary pc, can I snap in the fan and just have it working or will I have to apply thermal paste?

2. Would I be better off just getting a cheap $20 aftermarket heatsink even though the CPU is non-k and therefore cannot be overclocked?

I would greatly appreciate any feedback ASAP

Thanks! :)