Mesh Straining Bag

Would putting a fine mesh straining bag that you can pick up from Northern Brewer oxidize the wort if you were to put it over top of your racking cane?

I assume you mean over the rigid part that goes into the fermenter as you rack? If that's what you mean, then it's fine to do that. I've had trouble with it clogging, so I quit trying to do that, but I know others have had very good results with doing it just as you describe. I just rack carefully, and manage to not suck up any debris.

Well I just racked my first brew from primary to secondary. I just stuck the auto siphon down in tje fermenter and probably should have only stuck it down half way and then gone down further as the wort got lower. Going to work on my technique. Wife is really worries about too much sediment.

In a different thread it was mentioned that putting the hop sack/straining bag on the output end of your siphon when racking into the bottling bucket would help. I'm going to try that on my next batch and don't see any issues with oxidation since the flow would be the same as if the tube was just in the bottom of the bucket.

I tried a hop bag over the end but it kept getting clogged so I quit.
In order to minimize trub I prop my carboys up on my wing capper and put the autosiphon straight down onto the bottom corner. If you do not disturb the siphon, it will pull a tiny amount of trub at first then create a void that the beer can flow through without pulling trub. You can siphon out all of the beer right down to the trub.
Tell the missus not to worry about the sediment. It isn't anything that isn't in the beer already.