Straightening my step daughters hair?

Hey! So I've been in my step daughters life since she was a baby. Shes now 4 years old. She has beautiful curly blonde hair that I absolutely adore, but lately she's been asking me to straighten it (usually only when she sees me straightening my usually wavy hair) I asked my man for permission and he said it was totally fine, I just didn't want to over step even though he told me I didn't even have to ask because we both consider her my daughter as well but I am hesitant to do it. I would love the bonding experience with her, as we always sit down every morning together and I do her hair and she watches me do mine but I am worried about how her bio mom would react to this. I am currently pregnant with my first bio child so I have no experience with this sort of thing. How would any of you mamas react to this? Is it as big of a deal as I think it may be, or would you be okay with this? I dont want to cause problems by doing this, but I also feel bad for telling my step daughter no when he dad already agreed to let me do it. Picture of my beautiful girls curly hair. I would also like to add that we have 50/50 custody.