The status that you select on your W-4 is only for determining how much tax is withheld from your pay. It does not affect your tax return or whether you can claim the child tax credit. The filing status on your tax return does not have to be the same as the filing status on your W-4.
I don't know what "spouse requirement" you are referring to for the child tax credit. You do not have to be married to claim the credit. If you are married, your spouse does not have to be the child's parent. You can still get the child tax credit if you file as married filing separately.
