Books are a lot more dense than most other stuff (this is the reason moving boxes for books are a lot smaller than the other boxes). To stay under the weight limit you probably need to make sure the box remains quite small (very, very far from the maximum dimensions).
Books being heavy and cardboard boxes being fragile, you need to make sure the contents are well packed with no extra space which would lead to books moving around and potentially tearing through the box.
Cardboard boxes are quite sensitive to external stimuli such as being thrown around (manually or by luggage conveyors), having other luggage (with their wheels and handles) thrown against them or piled on them (imagine 4 or 5 bags weighing 23 kg each on top of your box), or meteorological conditions such as rain or snow (which they will be subject to between the terminal and the plane, I don’t think Ryanair use containers).
Remember that your box will be thrown around:
- By the luggage conveyor system between check-in and the holding area
- Onto carts
- Onto a conveyor belt into the plane
- In the hold
And the same thing in reverse at the destination.
So at the very least you need to make sure your box is:
Not too large in order not to be too heavy
Well packed so nothing moves around and the box does not get squashed if stuff is piled on top or pierced either by the books inside moving around or by the wheels of other luggage encountering “soft spots”
Well enclosed and protected, probably with lots of tape or film (possibly both), to manage the (not very careful) manipulations, heavy rain that could fall on it, and so on. Always remember to tape in both directions on all sides.
Adding “heavy” stickers on them (on all sides) is probably a good idea so that handlers don’t break their backs more than needed handling a box much heavier than its size suggests. It may deter the check-in agent though.
Remember that “handle with care” just doesn’t exist in the industry. Any such stickers will be ignored. Handlers don’t care about the bags, they just throw them around, and their only concern is trying not to get hurt doing so.
Also remember that handlers usually make use of handles on luggage. Here they will have to grab the box directly.
If the box looks flimsy in any way it will be rejected at check-in. If you can’t imagine it being forcefully thrown a meter or two away ten times, it’s not well packed. If you can’t step and stand on the box it’s not sturdy enough.
A final note: books seem to have a weird signature on scanners, and anytime we’ve had any significant quantity (much less than a boxful though), we’ve seen the bag opened and inspected. They will tear through any tape, and are unlikely to tape it back up correctly (if at all) afterwards. YMMV depending on the origin/destination and other parameters.
You may be better off carefully packing the books in a regular (but solid enough) suitcase instead of a cardboard box.