All your thoughts are correct. If the device was tested for compliance and passed, then the antenna had to be included in testing. Using a different antenna may affect the test results but I doubt it may cause more interference.
There are some classes of devices to be evaluated separately:
- short-range devices for specific frequency bands like garage or car openers. Their range is intentionally limited to say 100 ft by RF power generated and no larger or added antennas are allowed.
- e.g. Bluetooth devices may not be joined with external antennas to extend their range.
- there are "free" frequency bands like FCC No.15 standard in which the devices may cause interference to others and the user is advised to move a device away to resolve the problem, and devices may accept interference while the user may not call authority to resolve the problem.
I agree that your quarter-wave antenna can work better than a commercial antenna, only please use the available connector on your device to be sure no other than the desired signal is radiated. As you intend to sell the device with the new antenna, you will be responsible for the SYSTEM, and according to the particular standard you may be required to have the SYSTEM tested for compliance.
Compliance testing laboratory has to operate under national rules; I would recommend to ask the officials if and how the particular compliance rules hold for your case. Some standards are weak, some tough, depending on system class and frequency band used. Fines for non-compliance are high so it is better to follow the rules.