While you are fundraising for a great cause that many people can relate to this can be a tricky situation. Here are a couple of things I would consider if I were in your situation.
Is it ok to send these coworkers a request using the company email?
Some companies have a policy in place regarding selling products and soliciting fundraiser pledges. My first stop would be to the HR department, or a simple e-mail to the HR admin or whoever seems to be in charge of writing and upholding policies, in my company we don't have an HR department so I know that the Admin Assistant at the front desk usually handles these sorts of questions.
Many companies will review requests on a case-by-case basis and this is the first step. Having done this you may find that you are allowed to do an e-mail blast to the whole company, which could get you more money pledged.
Face to face
I'd like to engage these coworkers as well
It seems that you have only a few people in mind to ask, would it be possible to create run-ins with the ones that work in your building? I might go to their cubical or office to have a short social chat with them during the day. Your idea of targeting a few people may get more targeted pledges as people can see that you are passionate about the cause and want to help out a friend/coworker out. I would also prefer to do this in person then on the phone, phone conversation can be really nerve wracking, and you seem to be able to have held similar conversation with other coworkers, based how I interpreted on your question.
It seems that if you get a positive response from your HR department, you could also post a little notice in the lunch room or other common areas like elevator waiting area, front hall, or doorways to promote yourself and your cause. Seriously, everyone has had some contact with cancer in their lives, this is a worthy cause that touches everyones heart and you should have no problem in getting pledges if your company will allow you to solicit them.