I'd much prefer if you would not take my credit card number at all until I confirm that I want to convert from a free trial to a paying customer. I very rarely sign up for free services that require handing over payment information up front. After all, if you're legitimately offering a free trial, there's no reason you'd actually need my credit card number. If I lose interest in your free service after a few days, I don't want the hassle of having to remember to cancel to avoid a charge. I don't want to have to worry about being charged before the free trial is over (I've never heard of your company, so I don't know if you're honest). It just adds too much useless stress to the process. If I keep my credit card in my pocket, I know I'm in control.

Also, I think that the observation that you get much higher conversion rates from people who provide credit card info up front is debatable. It suffers from survivor bias: you might get a lot more paying customers from the group of potential customers who refused to sign up for your trial because you asked for payment info up front. That could be pushing away 95% of all your potential customers, but you'd never know it.