Is checking for key existence in HashMap always necessary?

I have a HashMap with say a 1000 entries and I am looking at improving the efficiency.
If the HashMap is being accessed very frequently, then checking for the key existence at every access will lead to a large overhead. Instead if the key is not present and hence an exception occurs, I can catch the exception. (when I know that this will happen rarely). This will reduce accesses to the HashMap by half.

This might not be a good programming practice, but it will help me reduce the number of accesses. Or am I missing something here?

[Update] I do not have null values in the HashMap.

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