Solvent for reaction mixture
Aluminium iodide ($\ce{AlI3}$) is first introduced in 1984 as an easily accessible, a highly regioselective versatile ether-cleaving reagent with novel cleavage pattern (Ref.1). Application of $\ce{AlI3}$ in organic synthesis has been reviewed (Ref.2) and it seems like acetonitrile is the best solvent to be used in catechol ether demethylation (e.g., 2-methoxyphenol or 1,2-dimethoxybenzene).

For example, recent article discussed an one‐Pot cleavage of aryl alkyl ethers by aluminum and iodine in Acetonitrile (Ref.3). Their proposed mechanism for the cleavage is depicted in following diagram:



Accordingly, since it needs acid work-up for final product, I'd suggest you may use acetonitrile as the solvent of reaction, and use your solvent of choice to extract the final product from aqueous work-out.

If you are not happy with that, you may use either carbon disulfide ($\ce{CS2}$), which is also toxic, or toluene (their are references have been in literature using benzene as a solvent with mixed results) (Ref.2). Use of $\ce{CS2}$ is applied for specific reactions such as substrates having allyl functionality. Yet, it should work with simple compound as yours. 

I'm little curious of your intend to use non-toxic solvent in the reaction since DMSO is also toxic in certain concentrations. In that case, you may use solvent-free conditions (you need to use enough DMSO for convenience, which is not critical according to the mechanism)(Ref.4). 

Note: Cyclohexane is not a suitable reagent for this reaction, although it was involved in some publications (Ref.3). For example, when demethylation of eugenol reaction has bee done in acetonitrile at $\pu{80 ^\circ C}$ for $\pu{18 h}$, hydroxychavicol was achieved in 78%. However, when the reaction was run in cyclohexane under identical condition, no hydroxychavicol was achieved. 



References:


M. Vivekananda Bhatt, J. Ramesh Babu, "New reagents 3: aluminium iodide - a highly regioselective ether-cleaving reagent with novel cleavage pattern," Tetrahedron Letters 1984, 25(32), 3497-3500 (https://doi.org/10.1016/S0040-4039(01)91058-5).
Juan Tian, Dayong Sang, "Application of aluminum triiodide in organic synthesis," ARKIVOC 2015, (vi), 446-493 (http://dx.doi.org/10.3998/ark.5550190.p009.309).
Juan Tian, Huaxin Yue, Pengtao Yang, Dayong Sang, "One‐Pot Cleavage of Aryl Alkyl Ethers by Aluminum and Iodine in Acetonitrile," Chemistry SELECT 2019, 4(1), 38-41 (https://doi.org/10.1002/slct.201803469).
Mehran Ghiaci, Jila Asghari, "Dealkylation of Alkyl and Aryl Ethers with $\ce{AlCl3 - NaI}$ in the Absence of Solvent," Synthetic Communications 1999, 29(6), 973-979 (https://doi.org/10.1080/00397919908086060).