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# [JavaScript (Node.js)], <s>80 73</s> 68 bytes

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 f=([x,...y],g=c=>f(y).map(z=>c+z))=>x?g(x).concat(x>'a'?g`^`:[]):[y]

[Try it online!][TIO-jybq428i]

[JavaScript (Node.js)]: https://nodejs.org
[TIO-jybq428i]: https://tio.run/##HclRCoMwDIDh4zRhmgMIqQfpOgyZLRuulSnSevluyP/wPfxvOWTT72vd@5Sfc2uBwZWOiKrvIivbABXpIyucbPV2IrItY4SCpDmp7FCsETPG6TENzuPgqm//s@VlpiVHCGD64@qeLgxi@wE "JavaScript (Node.js) – Try It Online"