You don't need a ton of credit cards, visa and mastercard check cards count, most everybody has one or two of those, and you can also use the prepaid gift type cards that many people use for traveling.
If you are looking at 70,000 miles, then a couple of three or four dollar fees for a prepaid credit card is money very well spent.
Doesn't show up on your credit report as a line of credit, no application, etc.