<<Disclaimer: Verify this information before applying it to your situation.>>

Here are some responses regarding soy sauce brands without wheat:-

San-J makes a wheat-free tamari

There are several brands that are GF including Krogers and San-J Wheat
Free Tamari to name only two. not Lachoy.  (doesn't have wheat in it)..

And here is a technical description of various soy sauces which may be
of interest - although no brand names:

There are two types of tamari: genuine tamari and shoyu tamari. Genuine

tamari is made from soybeans, sea salt, water, and koji (a culture of
lactic acid producing microorganisms). The ingredients are left to
ferment in large wooden casks for 2-3 years before filtered and
pasteurised.

Shoyu tamari also contains wheat as well as soybeans, water, sea salt,
and koji, and the fermenting period is usually only 2 years. Compared to
genuine tamari, shoyu tamari tastes slightly sweeter. Unfortunately,
some people intolerant to wheat and gluten react to shoyu tamari because
of the trace amounts of gluten sometimes present. This problem does not
occur with genuine tamari.

There is also soy sauce, which is Chinese, whereas tamari is Japanese.
Soy sauce contains the same ingredients as shoyu tamari and often small
amounts of sugar or syrup as well. Thus, it is less suitable for
allergics or people with dysbiosis.