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Whether you use a retainer (cage) or loose bearings, there should be two and only two contact points for each ball. There is no difference between the two in this regard.
I can't tell you what size balls you should be using, but the size of the old balls can be easily confirmed with a digital (or dial) caliper or with a micrometer. A reputable bike shop/mechanic will have one or both of these.
Regarding strength, if the retainer allows you to use the same number of balls as you would if they were loose, there is no difference in strength. (i.e. if you replace 11 loose balls with 11 identical balls in a retainer, they will be equally strong.)
Assuming you're using a reputable bike mechanic, I would follow his advice. If you feel strongly about sticking with loose balls, there's no reason he can't accommodate you, but you may have to pay to have him rebuild a perfectly serviceable bearing a second time. The retainers merely provide a convenience when assembling and maintaining the bearings.
Hope this helps.
If you want a second opinion, you can contact/visit Barnard's Schwinn in Oak Park. They specialize in vintage Schwinn restorations. They also carry NOS stock of lots of good stuff to help people get their bikes as close to original as possible.
FWIW, I have a 1973 Sports Tourer and the headset bearings are caged. This model was higher in the lineup. If it was good enough for the Sports Tourer, it should have been good enough for the LeTour. Then again, my bike may have been switched to caged before it came to me. Good luck!
From the Schwinn catalog in 1974, it looks like the "10-speed" road bikes from best to worst (least best?) are:
1. Paramount
2. Sports Tourer
3. LeTour
4. Continental
5. Sprint
6. Varsity Sport
I'd put the Voyageur II (in the back of the catalog) around the quality of the Sports Tourer. Also, it's amazing how much lighter the Paramount is than all the others.
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