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Although both the idioms "to nibble at something" and "to nibble on something" have the meaning of eating by small bites, in the former that something is always some kind of food, whereas in the latter in may also be something that you bite but not break its surface.

Examples:

The rabbit nibbled on/at a carrot.

Fish were nibbling at the bait

He nibbled nervously on his fingernail.

So regarding your sentence, there's no difference; although I'd prefer "nibble at".

Although both the idioms "to nibble at something" and "to nibble on something" have the meaning of eating by small bites, in the former that something is always some kind of food, whereas in the latter it may also be something that you bite but not break its surface.

Examples:

The rabbit nibbled on/at a carrot.

Fish were nibbling at the bait

He nibbled nervously on his fingernail.

So regarding your sentence, there's no difference; although I'd prefer "nibble at".

Although both the idioms "to nibble at something" and "to nibble on something" have the meaning of eating by small bites, in the former that something is always some kind of food, whereas in the latter in may also be something that you bite but not break its surface.

Examples:

The rabbit nibbled on/at a carrot.

Fish were nibbling at the bait

He nibbled nervously on his nail.

So regarding your sentence, there's no difference; although I'd prefer "nibble at".

Although both the idioms "to nibble at something" and "to nibble on something" have the meaning of eating by small bites, in the former that something is always some kind of food, whereas in the latter in may also be something that you bite but not break its surface.

Examples:

The rabbit nibbled on/at a carrot.

Fish were nibbling at the bait

He nibbled nervously on his fingernail.

So regarding your sentence, there's no difference; although I'd prefer "nibble at".

Although both the idioms "to nibble at something" and "to nibble at something" have the meaning of eating by small bites, in the former that something is always some kind of food, whereas in the latter in may also be something that you bite but not break its surface.

Examples:

The rabbit nibbled on/at a carrot.

Fish were nibbling at the bait

He nibbled nervously on his nail.

Although both the idioms "to nibble at something" and "to nibble on something" have the meaning of eating by small bites, in the former that something is always some kind of food, whereas in the latter in may also be something that you bite but not break its surface.

Examples:

The rabbit nibbled on/at a carrot.

Fish were nibbling at the bait

He nibbled nervously on his nail.

So regarding your sentence, there's no difference; although I'd prefer "nibble at".