AFAIK, 17" scale length would be classified as 1/4 'fractional' guitar, and 19-20" scale would be 1/2 'fractional' guitar, 23" scale would be either 3/4 or 7/8 size, and as such, examples of strings available for these sizes can be seen here:
Strings By Mail - search results - fractional guitar
If you take standard classical guitar strings, for (4/4) 25" scale length made for EADGBE tuning and put them on a shorter scale, for example like the 17" of the Yamaha GL-1 Guitalele, and tune them to EADGBE, they will have such reduced tension, and be so floppy and unplayable, and not hold pitch as well as sound very bad if there is even enough tension to render a note. I have done this and it is not useable as such.
Just strumming or plucking will detune the note sharp, as will fretting since the strings are so floppy, not pleasant sounding at all.
If this were for a beginner, you would never learn to tune the guitar properly since the strings do not have enough tension, and this will discourage a new player right away.
For myself, I ended up tuning the standard scale strings (Thomastik-Infeld CF128 -
http://www.stringsbymail.com/store/thomastik-infeld-cf128-classic-n-superlona-full-set-2181.html) up to ADGCEA and just use it that way. The reason for my using these strings is that they are 4 FLATWOUND strings and 2 nylon strings, and reduce significantly (but not totally) the string squeak noise, and I have not found classical guitar fractional strings that are BOTH flatwound/polished, AND for 17" scale length with proper tension for EADGBE tuning on the shorter scale.
If you are set on using standard classical strings, you could try the D'Addario EJ44C strings set that includes 2 different G strings for you to try:
(
http://www.stringsbymail.com/store/...omposite-extra-hard-tension-full-set-115.html)
which are 'extra hard tension', or the Savarez Yellow card
(
http://www.stringsbymail.com/store/...earch_in_description=1&keyword=savarez+yellow)
either of which *MAY* or may not work - as per recommended by others elsewhere here in the forum. I have not tried them yet myself.
However, La Bella has been making classical guitar strings since forever, and I would probably go with the La Bella FG114:
(
http://www.stringsbymail.com/store/la-bella-fg114-fractional-guitar-1-4-size-full-set-798.html)
as a starting point, but you need to match the scale length of the instrument to the strings set to get the proper tension, and each set shown in the search results linked above (first link in this post) tells you the scale length or instrument size you can use them on.
If I am not mistaken, the Southcoast EFS strings that Jim mentions have the 3 'bass strings' (i.e.) the ones closest to your face, an octave ABOVE, (re-entrant) so while chord shapes are the same, the sound will be very different from an adult size guitar (brighter and higher), with pitch reference thus:
E3 A3 D4 G3 B3 E4
as opposed to what it sounds like you want in standard pitch range of a ~25" scale guitar:
E2 A2 D3 G3 B3 E4
For a sound sample you can watch fellow UU member Dr. Bekken's 4 videos with this string set:
http://forum.ukuleleunderground.com/showthread.php?98296-Southcoast-EFS-Guilele-String-Set
http://forum.ukuleleunderground.com/showthread.php?98399-You-Gonna-Need-Somebody-On-Your-Bond
http://forum.ukuleleunderground.com/showthread.php?98437-Eddie-Freeman-Special-Rag
http://forum.ukuleleunderground.com/showthread.php?99208-Bottle-Up-amp-Go
Hope this helps!