You don't want it to NOT have an odor. Have a pipe dedicated to a tobacco type. I'm an aromatic fan so I have a pipe specifically for cherry, so it smells oh so faintly of cherry all the time, which is nice. You really should own a few (I have dozens) for various reasons, such as a travel pipe, one dedicated to berry-flavored aromatics, an English blend one rich with Latakia (it's pungent).
Tobacco will ghost your pipe a tiny bit (Captain Black Cherry is an unruly MONSTER at this like Cherry NyQuil in a bad way). Clean as you might, the hint of tobacco will be omnipresent even if you sanded down the interior of the bowl. You WANT this though. You WANT it to create carbon char and have a tiny bit of odor (not the stem, just the bowl). Allow it to set up. This is how a pipe lives and wants to live. Let your pipe live.
Consider panties.. oh, wait. Wrong forum.