On a 22-23" scale, to get an octave below with steel strings, you are looking at at-least 3 wound strings of something like 0.052", 0.042" 0.032" and a plain 0.022" in order to have the approx 22 lbs of string tension (per string) required in order to have ANYTHING close to decent intonation (similar to the D'Addario EJ80 octave mando strings), and then you are also likely going to need to look at compensating your saddle LONGER any way because the thicker strings will still have intonation about 15 cents sharp, and then is the struggle of recutting your nut slots for the thicker strings, and then fussing with the truss rod to eliminate string buzz and to compensate for the approx 80-90 lbs of string tension, which is actually more than the ~60 lbs of string tension with CGDA or DGBE tuning with using the D'Addario J66 strings...
If it was using classical guitar strings, they will definitely all be wound, and something like 0.060", 0.052", 0.044" and 0.038" for octave uke tuning on 22-23" scale, and still only about 65-70 lbs of tension, but maybe not so much saddle compensation required as with the steel strings. La Bella makes a set of 'Contra Bass' classical strings meant for 27" scale length spanish guitars meant to be tuned like a piccolo bass E-A-D-G, that might work if you cannot get singles.
Strings By Mail has both of these D'Addario sets I mentioned, and also the La Bella sets, but Strings And Beyond will not have these 'Contra Bass' strings but do carry the D'Addario sets too.
Both were having 15-20% off on their sales for Black Friday/CyberMonday but I'm not sure if the sales are still running now.