Blue tit nest box under siege

Hello everyone, we have a pair of blue tits happily housed in our nest box which has become of interest to a local cat. Today I saw it sitting on top of the box whilst one bird was outside 'shouting' at it and the other remained inside the nest. I chased the cat away but am keen to prevent it coming back. As the birds are using it would attaching some sort of spiky twigs around the roof area suffice and not disturb the birds?