You could use a low-poo with coco betaine, that would remove cones without needing sulfates.

Also, some hot oil treatments are meant to be used before a shampoo, so you might want to check the instructions. Plus, even if those aren't the directions you could still do it that way, or just wait until you are ready to wash it and low-poo it out.
Or clarify, if you are due for one!
2c/3a/3b, Fine/med, Dense, high porous, & normal elas.

Lo-poo - Renpure Keratin, SMR, Giovanni SaS
clarifying - mix Johnson's H2T with low poo
Co-wash - Suave Nats. clar. or coco.
RO - GVPCB, Ion Eff. Care, TN.
LI - SMR, Cure Care, or RO
Seal - MO or Jojoba
DT - + honey, ACV, & EVOO to SM masque & GVPCB
PT - Gelatin!, CNPF
Styling - FSG, AIF, BRHG, LALS/PS, GF curl spray gel, SM Souffle/Smoothie, LOOB
Oils - MO!, EVOO, jojoba, GSO, SM Elixer, EVCO, VO5 Hairdressing