I'd also vote leave it alone. Darker toning like that can be very hard to completely remove and you could end up diminishing the coins appearance overall.
To me the operative word in your question is - I. And my answer to you would be - not unless you know what you're doing. But should the coin be dipped ? That's a complicated question. First of all the coin looks to be AU and as such of no value to speak of. Secondly the coin, even in MS65 could easily be replaced for about $20-$25. Then there is the question of has the toning already damaged the coin ? On the obv right hand side in particular the toning looks to be black and quite heavy, so even if dipping was done correctly there may already be damage underneath the toning. If there is then the coin is not even worth AU value. But let's assume for the sake of argument that there is no underlying damage, the question then becomes what would you have if you did dip it successfully ? Answer, an AU common coin. But if you do not dip it, then at some point in time that heavy toning already existing is going to damage the coin. That is a given. So even though the coin has no value to speak of, it is a certainty that in time it will be of less value. So if you like the coin for your own reasons, then to protect it from any further damage, then yes it should be dipped. But only by somebody who knows what they are doing. This is kind of the thought process you need to go through when you ask yourself a question like that. And I may be wrong but I'm assuming that's what you really wanted to know.
I don't necessarily want to. I got the answer I was looking for from your (and others) reply. Thanks! (edited to fix quote tags)