Yes, it is very much possible. Thousands of sellers are selling product on Amazon without opting their fulfillment service. All you will need is to register as a seller, list your items, set shipping charges as per your preference, Amazon will charge fees 15% on each order, that's it.
Yes, you are right. The conversion of FBA items is far better than items fulfilled by merchants. And moreover, there are Prime members who in general would like to buy FBA products. If you want a clear edge and lots of order then it is advisable to go for FBA. Still, there are many sellers with unique items (no direct competition), competitive price is doing a lot better without opt-in FBA.
You are not required to use FBA to sell on Amazon. You can fulfill those orders from your own warehouse. They call this FBM (Fulfilled By Merchant).
Where this gets more interesting is that sometimes Amazon will require you to print shipping labels for those orders through the Amazon API. This requirement is called Seller Fufilled Prime (SFP). This way Amazon doesn't physically manage your inventory, but Amazon is directly involved in how your orders are being shipped (because shipping labels are created through Amazon API).
You can sell on Amazon without availing FBA, there are two ways through which you can do this -
1. Fulfilled by Merchant (FBM) - In FBM, you get to manage shipping, returns and customer service. Recommended for made-to-order products as creating and holding inventory required for FBA will be a costlier approach.
2. Seller Fulfilled Prime (SFP) - A lot of users go for prime products only, when purchasing products from Amazon. FBM puts you in a tough spot here. You can still qualify for the prime program with SFP provided that you qualify the fulfillment standards defined by Amazon.
More details here