Chloroform is a trihalomethane (THM) and is a disinfection by-product when using chlorine, but it is the least problematic of all the THMs. Though it can be absorbed through the skin and inhaled in breath, it is also exhaled and excreted and most importantly it is not cancer-causing or mutagenic until it reaches very high cytotoxic levels far far higher than found in even the worst-managed pool or spa (technical details in
this post). The information you have been reading about chloroform is old and inaccurate and are most likely on websites with a financial interest in selling "alternative disinfection" products. The THMs of concern are the brominated ones so when you have a choice, you could use chlorine instead of bromine and can see if your fill water content is low in bromide.
If you follow the principles on this forum in terms of chlorine maintenance, then the active chlorine level will be very low due to the use of Cyanuric Acid (CYA) in the pool that significantly lowers chlorine's strength to the equivalent of around 0.1 ppm Free Chlorine (FC) with no CYA. This reduces the rate of creation of disinfection by-products as well as the rate of oxidation of swimsuits, skin and hair. Also note that the amount of disinfection by-produts is generally a function of bather-load and that this is very low in residential pools. Finally, if the pool is outdoors exposed to the UV in sunlight, then the breakdown of chlorine produces hydroxyl radicals which are very powerful oxidizers -- ozone and hydrogen peroxide both likewise break down to hydroxyl radicals though they obviously don't form chlorinated disinfection by-products.
If you wanted to use the lowest possible chlorine level, then you could use an algaecide such as Polyquat 60 to control algae growth and then have the chlorine level be lower than needed to kill algae, so could have an FC that is only 2-3% of the CYA level so roughly equivalent to 0.02-0.03 ppm FC with no CYA. A similar alternative to control algae, but that can get expensive, is a phosphate remover.
Nevertheless, if you want an EPA-approved non-halogen (no chlorine, no bromine) system for the pool, then PHMB would be your only alternative, but it is expensive and has problems over time, though the first year or two will generally be OK.