As asked by Kate1 where have you got your data from?
I realise that you have said you feel nervous about calling first but it might just be your 'script' that is holding you back. Try different tactics, different wording, don't beat around the bush, but don't rubbish there existing site, they might love it or have designed it themselves. Have some notes to begin with and after a while it will just fall off the tongue. Don't worry about rejection there will be loads. Set yourself personal challenges, set a whole day aside for phone calls, not just an hour here or there. Challenge yourself to making five or six appointments in that day. You could get 1 app early and none for 5 hours then 4 in the last hour, it happens! Treat it as a game. If 2 apps are for next week don't include them in your figs, keep going... Set aside that time again next week on the same day, keep going...
For you, (in your situation), I would call first, speak to the decision maker, explain briefly who you are, and the benefit of an appointment, without obligation (if prospecting locally) if not then email or send info in the post, to a confirmed email address, so that it misses the spam filter. Follow up again, next week as part of you weekly calling session.
For myself, (in my situation)
all I require is an appointment from my phone call. I dial on a Monday as it works for me. Some days one script works better than another for me, I can chop and change through out the day. As a very last resort I send more info, if they will not have an appointment.
They say there are three types of person, one who will never buy, one who will buy and one that might buy!. But there is also one other, that is all of us!
We all buy
The above works for me, so might be worth a try...