How to soften a bra band

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Hi all, how can I soften a band on a bra? My daughter struggles to get a fit because she is a tiny band size but large cup and she likes non wired. We’ve found ONE that fits great but she says the band is too itchy (she has a sensory processing disorder). Could I easily line it? Or soften it in some way?
 

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Other than washing it a couple of times I am not sure what else you could do to soften it without ruining the bra
 
Can she wear a vest under it?

Or that spray you get to put on your skin to stop shoes giving blisters?