Two bio-based solvents, natural deep eutectic solvents (NaDESs) and γ-valerolactone (GVL), have been used under microwave (MW), and ultrasound (US) irradiation to design an efficient and sustainable process for wheat straw delignification and have been compared with the traditional alkali procedure. Best delignification (45%) was achieved with a three-component NaDES (lactic acid/glycerol/choline chloride) under MW irradiation (at 120 °C in 30 min), with solid/liquid ratio of 1:50. A GVL/water mixture (8:2) also gave an efficient delignification (27%) under US irradiation (40 kHz, 200 W) at 50 °C for 60 min. Analytical pyrolysis (Py) coupled with GC/MS/FID, provides valuable information on the extracts’ chemical profile. DPPH and Folin–Ciocalteu tests highlighted the efficiency of MW- and US-assisted extraction as well as the extracts quality. The highest antioxidant activity for the NaDES extracts was obtained under US irradiation.