Shipping integration advice

I am setting up a Woocommerce site that will contain over 20,000 products. I only have product weight meta-data. I do not have dimensions for all of the products. I would like to know if anyone can suggest a method to handle shipping of products upon checkout given I don’t have dimensions. Is there a best-practice shipping solution for my scenario? How are others handling it? My products range from small cables that weigh almost nothing to a consumer-grade printers weighing up to 40lbs. I would like to integrate with a Fedex/UPS/etc. Is there a Woocommerce solution that enables me to charge shipping strictly based on weight?