“Need” is a relative term.
Do you need a preservative, as in “Is my product at all likely to get contaminated under the majority of conditions it will come in contact with?”
Or, do you need a preservative, as in “Am I likely to get sued if my product gets contaminated in an unusual situation?”
Or lastly, do you need a preservative, as in “Am I likely to get in trouble if the regulatory agency in my country finds out that my product got contaminated in an unusual situation?”
The detailed answer I usually try to give is that if you are the only person that will ever use the product, and if you are comfortable taking the risk that your product might be moldy and/or bacterially contaminated, then it’s possible that you won’t do yourself any permanent harm with the product if you don’t use preservatives. But I strongly advise you (and everyone) to always use preservatives - you never know what could accidentally happen, or to whom.
It’s a bit like asking your doctor “Do I need to take these antibiotics?” after he’s diagnosed you with a bacterial infection.