Security risks of disabling "Find my iPhone"?
The security risk you endure is that you won't be able to trace the device location, and use the functionality in Find My iPhone for erasing the device, adding a message and giving off sound. 

In addition it is possible for others to format the device and start using it with a different Apple-ID. However this is not a risk to the confidentiality your data or your accounts - they would need to do a factory reset (i.e. delete everything from the phone) before doing this.

I would advise backing up the unit before handing it over for repairs at the very least. If you want absolute safety, make sure that your phone is completely emptied before sending it. You do that from Settings > General > Reset > Erase all content and settings. 

Assuming that you trust the repair partner to not steal your iPhone, I would say that the only real risk associated here is what happens if someone breaks in and steals your iPhone from the repair partner's premises. In this case your data is not anymore at risk than it was before, but because you have disabled Find My iPhone - you cannot track your phone, and it can be repurposed for a different user.