Other than the free search , which you have already tried I think , there is no way of accessing the 1939 Register without subscribing to FindMyPast. We are not allowed to do look ups on your behalf because of strict copyright regulations.
The guidance on their site is that individuals records remain closed for 100 years from their date of birth. For those born less than 100 years ago records may be opened if proof of death is established. (There are instances where mistakes have been made , either in redacting records incorrectly or making available records which should have been redacted .)
You could try broadening your search terms and looking for other family members , as has been suggested. It is quite common for birth years to be out by a year or two in the Register.
