There’s always iodine tincture- its just iodine and alcohol at about 3x the concentration used for water purification.
A lot of hard-core survival kits actually explain how to mix this stuff up using the water purifier drops or tablets in the kit, and its basically the bootleg form of the most common surgical antiseptic, betadine. That stuff adds a stabilizer to reduce toxicity, but the old school form of it works just fine for first aid on anything not requiring reattachment of limbs or open chest surgery.
Also, on the peroxide thing: The problem isn’t that it isn’t a great antiseptic. The problem is that it is TOO good at being an antiseptic. HO-OH kills EVERYTHING it touches at concentrations above a few percent. The stuff you get at a store doesn’t kill bacteria reliably because its only 3% solution- that concentration can actually speed healing, so long as you don’t keep reapplying it, and is a great cleaning agent to use before applying a long-term antiseptic. ~6% solutions still get used medically as a “nuclear option” for wound care, especially in field medicine for gangrene where you want to chemically cauterize the wound at the same time that you flush it out, and concerns about shock are a moot point. 10-30% solutions are one of the standard ways of cleaning surgical tools, because it dismantles most organic molecules at those concentrations. They use concentrated peroxide vapor to decontaminate quarantine zones. Its a phenomenal antiseptic. The problem is that people are made of the same stuff as bacteria. X3