I would like to know suggestions or wallets that can help mix the coins and we loose track of the chain analysis. I am free to convert my bitcoin to any other currencies and then convert back, even flexible to move coins between exchanges (centralised ones), but what I would not like is to use any mixers or any online exchangers.
Any suggestions / tips?
Note: I hope it is not against the forum policy to discuss this

So, you don't want to use mixers and instant exchanges, right? I'm curious about why you don't want to use instant exchanges because they are your best bet in this case but anyways, let's continue with the given requirements.
CoinJoin is your best bet, either with your wallet or with 3rd party CoinJoin wallets but keep in mind that if you deposit Coinjoined Bitcoins to a centralized exchange, you might be banned. Maybe find a person who wants to buy something with Bitcoin and instead receive an altcoin from them or find a person who wants a Bitcoin loan and receive new Bitcoins from them to a new wallet when the payment date comes. There are many things that you can do if you turn on your creativity but I'm not gonna write them because they sound too good and abusable.