Hi Linda,
It's quite simple really, and other than maybe 1-2 string makers, every string making company that I've encountered (that I can remember), lists the string diameters on the package, as well as the web site selling them.
stringsandbeyond.com and also stringsbymail.com both show the PICTURE of the string pack, and ALSO include the diameters in the descriptions.
I'm not sure how you are
not seeing string diameters, unless you are only buying from certain companies that do not care to share this info about their strings.
D'Addario lists all gauges here:
http://www.daddario.com/DADProductsUkulele.Page?ActiveID=3781
for ^ you have to select the STRING TYPE by clicking the picture of the string pack, and then in that page you get after, you can select FAMILY TENSION CHART and is shows you the info of string diameter and tension, and currently D'Addario has 6 different SERIES of strings, and each have a different chart, but NYLON will be thickest and FLUORO will be thinner...
Living Waters here:
http://www.kenmiddleton.co.uk/living-water-strings/
Worth has over 20 different sets listed here:
http://worthc.to/english/w_strings.html
Martin here:
https://www.martinguitar.com/strings/ukulele/
Other brands are from the vendors up in the text paragraph, and both stringsbymail and stringsand beyond each sell more than a dozen brands of ukulele strings, and each has at least 4-5 different sets.
Fremont and PhD string diameters can be found on Uke Republic here:
http://cargo.ukerepublic.com/category/strings
Also, check these, and be prepared to spend an hour or two:
https://www.stringsbymail.com/ukulele-strings-684/
http://www.stringsandbeyond.com/ukelele.html
Also, if you still have 'viewing forum signatures disabled' you will not see the link that I have in mine, so I will include it here, since it might be helpful for you:
http://forum.ukuleleunderground.com...-String-Recommendations&p=1981276#post1981276
Hope all of this helps!