There are a number of alternatives to luggage locks but there is a reason why they are not often discussed. They are not as effective as travel padlocks when it comes to securing your luggage.
The 2 main alternatives to travel locks are:
Zip ties are also known as cable ties are are strips plastic that can be used to bind things together.
Plastic wrap which is very similar to cling film is used to wrap the suitcase. The suitcase is covered several times in all directions in the plastic wrap, usually with the assistance of a device which spins the suitcase.
If for any reason security officials wish to inspect your luggage they both have a big headache in either situation whether you have used zip ties or plastic wrap. In both instances the officials require i sharp knife to cut the cable ties and slice through the plastic wrap. In either situation your precious luggage might be damaged. As well as the potential for damage if your cases are opened the plastic wrap and cable ties cannot be reused so your belongings will no longer be secured in your luggage.
Even if security officials don't have to open your cases you are still face with the tedious task of removing either the cable ties or the plastic wrap.
It is far simpler and quicker to use a TSA Approved padlock which can be reused. There have been so many times that I have been in the checking queue and I have realised that I needed something from my case so I have unlocked my suitcase. NOT possible with cable ties and plastic wrap.