Are you specifically looking to achieve/maintain your own certification against a specific food safety scheme (BRC or similar), or is this "just" for the purposes of your own due diligence and HACCP requirements?
You can possibly demonstrate that your own process addresses certain types of risks, if you have sufficient validation in place - for some it should be fairly feasible to find scientific papers to substantiate. It certainly sounds like your process may help with some microbiological considerations, but does it address e.g. potential spores, and is this a risk for your products and ingredient types? (Don't readily recall seeing anything on heat and ethanol combined, but from memory there are some Bacillus spores that will survive high ethanol concentrations).
Obviously there are also some types of hazard for which it probably won't help - physical contaminants, potentially chemical/allergen, etc, along with the authenticity and food defence aspects that Lesley noted.
We used to have a reasonable number of non-GFSI suppliers but thankfully this has declined very significantly over the last ten years.
I agree with Lesley's advise that an SAQ can be used for genuinely low-risk suppliers, and/or to get an initial feel for a site's capabilities, but you may also need to consider auditing them yourself. It's not clear if you meant that these suppliers have no HACCP certification, or no HACCP system at all - the latter is obviously somewhat more of a challenge.
Just be careful about what you ask, and how you ask it!
Some years ago we were looking at a processor who was very proud of their controls for physical contaminants in raw materials. It turned out that this was a mass of incandescent light bulbs over their raw material receiving area - the intent was that it gave good visibility so their staff could spot twigs etc coming in with fruit crops, but these were basic domestic bulbs with no shatterproof coating and no covers, placed directly over open unloading silos. No consideration had been given to the potential hazard the bulbs themselves introduced, so there was no register or inspection process, and at least one bulb was missing. They were not approved as a supplier...
GFSI-benchmarked schemes may not be perfect and aren't essential for a supplier to be suitable/competent, but theoretically they do at least force sites to consider some of the more relevant basics 
