If you are looking to only hide the select menu, you could try using the following CSS to see if it meets your needs:
table.profile_table_editing span#pronouns {
display: inline;
}
span.edit_data select#user_pronouns {
display: none;
}
Keep in mind, since the permission is enabled to edit pronouns, custom CSS and/or JavaScript can limit the ease of access to edit, but it wouldn't be 100% effective.
I would also recommend checking the mobile apps to see if there as option to edit in the mobile app. If there is, this is good to be aware of since you likely won't be able to use any CSS or JavaScript to hide it. Unfortunately, customizations for mobile apps is very limited.