I've almost made a living out of being peoples Best Man etc (not being a dick about it - honest) so I have read a lot of verses (religious and not) at weddings and done many speeches and I have one, overarching view.
Irrespective of whether I am at a Christian wedding, a Sikh one, a Church one or in a Registry Office - I consider every time I am asked to take part in someones (hopefully) most memorable day very seriously.
It's not for me to impose MY religious views on them, but for them to invite me to participate in theirs. I'm non religious and lord knows (hehe) most people who have met me here know I am about as offensive as a used jonny stuck to your shoe, but Wedding's need to be done right....
So, here is what I have to ask you mate - is your sister religious? Does she WANT a religious reading or does she just want you to be there and to participate because she loves you and wants to make you part of the celebration?
If the first, then Alan is prob the best man to be helping you as he clearly knows things I don't, but I would say this - DO read the religious verse and do it seriously and as she would want it. Give it 100% for her mate.
On the other hand, if she just wants you there, then you have some freedom to do as you like and I promise you this - she will thank you all the more for making it your own. Some of the most popular readings I've done were ones I wrote myself, whilst others were exceptionally fitting love poems or stories I had read or searched online for.
If this is the case mate then PM me some details and I will gladly help you out if I can!!