Joseph
no absolutly not, that would be chukas akum unlike Presents which are a basic human expression of celebration/thanks/appreciation/joy etc. much like having a party/singing/eating/smiling etc non of which are assur on chanukah even though Goyim may do it on their holidays
(You also lied when you said it was my family tradition. You can easier make a case that lying is chukas akum more than chanukah presents)
Now your turn:
did you get christmas chocolate this chanukah?