Hello and thank you for your question.
The noise is probably not due to the size of the plug. All standard plugs should be verly close to the same size (1/4"), and the jack contacts are spring loaded so they tend to compensate for any variations. There are three much more common issues that will cause what you describe. Oxidation on the jack contacts, a broken jack or problem with the the jack connections to the circuit board, a bad cable.
Oxidation on the jack contacts is basically a film that builds up and makes areas of the jack less conductive, so you get an intermittent connection. Put some rubbing alcohol on a plug and plug it in and out of the jack few times. If this seems to help a little then the issue is oxidation on the jacks. Special contact cleaners like De-Oxit will clean out the jacks even better than alcohol, and that is the route I would recommend.
If the plug feels very loose, the jack may be broken or worn out. if the jack itself wiggles a lot, then you may have broken solder where it connects to the board. Either issue would require opening the unit and repairing it.
Finally, the most common cause of noise is a broken cable. Cables tend to break right where they go into the plug housing. To check if the cable is the problem, wiggle the cable with one hand while holding the plug still with your other hand, so that it does not move around inside the jack. If it still crackles and cuts out, then the cable is the culprit.
I hope that helps. Please let me know if you have any other questions regarding this issue.