Generally not, however some brokers may allow it. My previous CFD Broker - CMC Markets, used to allow you to adjust the leverage from the maximum allowed for that stock (say 5%) to 100% of your own money before you place a trade. So obviously if you set it at 100% you pay no interest on holding open long positions overnight.
If you can't find a broker that allows this (as I don't think there would be too many around), you can always trade within your account size. For example, if you have an account size of $20,000 then you only take out trades that have a face value up to the $20,000. When you become more experienced and confident you can increase this to 2 or 3 time your account size.
Maybe, if you are just starting out, you should first open a virtual account to test your strategies out and get used to using leverage. You should put together a trading plan with position sizing and risk management before starting real trading, and you can test these in your virtual trading before putting real money on the table.
Also, if you want to avoid leverage when first starting out, you could always start trading the underlying without any leverage, but you should still have a trading plan in place first.