First, There is not “A non-chlorine bleach” — there are many.
Second, “chlorine bleach” is not “liquid chlorine”. Liquid
chlorine is the liquid for of the element chlorine which boils at
about -29F. Do not confuse “chlorine bleach” with “liquid
chlorine”. Chlorine bleach is a solution of sodium hypochlorite,
and it is the hypochlorite that is the active ingredient.
Third, it depends upon what microbes are the target of the
disinfection. Some agents work better on some microbes than other
agents. Note: here I use the term “microbe” as a generic term
referring to viruses, bacteria, mold, spores, etc. all lumped
together, even though they are very different. In practice, some
disinfecting agents may be more effective against some types of
“microbes”, and other agents are more effective against other forms.
There are several readily available substances that are used in place of hypochlorite bleaches.
Hydrogen peroxide is commonly used as a disinfectant and it
is very effective against many microbes. Its mechanism is a rather
complicated decomposition of the hydrogen peroxide into various
intermediates before ending up as molecular oxygen, which is why it
foams when you rinse your mouth out with peroxide. Its shortcoming
is that it tends not to be too stable once the bottle is opened.
Alcohols: usually ethanol (grain alcohol) or isopropanol
(rubbing alcohol) are both very effective disinfectants. Their
shortcoming is flammability and toxicity if ingested.
There is an entire class of chemical substances with the
daunting name “quaternary ammonium salts” or “quats” for short.
There are used in a variety of hand and body wipes. They are
relatively non-toxic (to humans), stable (to light and air), and
effective against a wide range of microbes. They are frequently
used in combination with an alcohol in hand and body wipes. But
they are also used in surface cleaners like “Envy” (this is not an
endorsement, but only used to identify a type of product).
These are only a few of the substitutes “out there” for
non-hypochlorite disinfectants. That field is a large area of
on-going research and development by companies who make those types