Disclaimer: I am neither a medical doctor, nor an expert on making liquor or on this kind of brewing, nor a scientist.
Sorry, I am not sure this will work for you, in my uneducated opinion, unless you plan to use only fructose in your liquor. (I am assuming that fructose is safer for diabetics, and you are OK ingesting it, even though I believe the jury is still out in terms of the advisability of long-term use of fructose by diabetics.)
Background: The brewing (and liquor-making) process works by having brewer's yeast or distiller's yeast 'eat' sugars, with the major byproducts being alcohol and carbon dioxide.
Problem 1: The types of sugars that brewer's and distiller's yeast generally eat are the same types of sugars that provoke insulin response in diabetics - monosaccharide sugars (glucose, fructose, and galactose), and some disaccharide sugars (such as sucrose and maltose). They do not ferment sugar substitutes such as aspartame, sucralose, stevia, saccharine, cyclamate, sorbitol, xylitol, other sugar alcohols, or acesulfame potassium.
Problem 2: Yeast also do not fully metabolize all sugars even if they are the kind they eat, and they leave behind sugars that would be a dietary risk for diabetics. It is common for them to leave behind 20% or more of sugars in beer and undistilled liquor.
So maybe you can make a liquor with no malted barley or other malted grains, and only fructose in solution with some sort of liquid (mix pure fructose in water). You could ferment it with brewer's yeast or distiller's yeast (e.g, alcotec turbo yeast). Not sure how that will taste. My wild guess is that you will end up with a pretty harsh liquor that is up to 14 percent alcohol, depending on how much fructose you use.
BTW, I also not versed in liquor laws, and this is not legal advice, but I believe that federal law prohibits home distillation of liquor without a permit. Making of beer and wine at home for household use is permitted.
Conclusion: Thus, the issue is not whether you can cook sugar substitutes and put them in a beer/liquor-making process. But rather that the yeast will not ferment sugar substitutes.