Replacing pneumatic bicycle tires with Honeycomb Hole non-pneumatic tires
Most likely the 24" 1 3/8" tyres will not fit on you bike with 24" x 1.95" tyres. While the inch diametre is the same, decimal and fractional number usually mean different standards for tyre sizing.

Sheldon Brown provides tables with sizes. Here is an excerpt:

24 x 1.5-24 x 2.125 | 507 mm        | Juvenile mountain bikes, cruisers

24 x 1 3/8          | (E-5) 540 mm  | British Juvenile, most wheelchairs; 
                                      common on women's utility bicycles in Japan.


Please check if your tyres provide also an ETRTO number, such as 50-540. ETRTO numbers give the nominal tyre width followed by bead circle diametre, also in milimetres.

If the larger number matches, the tyre is intended for a rim of the same size.

At that point you have to check if rim and tyre width are compatible and if the tyre clears the frame and brakes. Both are usually not an issue when the sizes are about the same. Unless you have very little tyre clearance with your present tyres already.