To reiterate what russellhltn is saying: A baby blessing does not have to be recorded (or even performed) to create a membership record.
I suspect there is a common misconception that a baby blessing is required for a record to be created because many blessings include "and the name by which (s)he shall be known upon the records of the Church is ...." That doesn't mean that ordinance has to be performed before a membership record can be created.
Here is what the General Handbook says:
For statistical and reporting purposes, the following individuals are members of record. Each of them should have a membership record:
General Handbook: Serving in The Church of Jesus Christ of Latter-day Saints, 33.6.2
- Those who have been baptized and confirmed.
- Those under age 9 who have been blessed but not baptized.
- Those who are not accountable because of intellectual disabilities, regardless of age.
- Unblessed children under 8 when (1) at least one parent or one grandparent is a member of the Church and (2) both parents give permission for a record to be created. This includes children of converts. (If one parent does not have legal custody of the child, the permission of the parent who has custody is sufficient.)
Note that the case of unblessed children is specifically documented there: "Unblessed children under 8..." There is your handbook reference that a blessing does not have to be performed.
The baby blessing is NOT recorded on the membership record. It is not an ordinance that is necessary for salvation and exaltation. (See General Handbook
, 18.1 and 18.2)
If a baby blessing is performed in another ward and the parents want a certificate, you can (and must!) create the record and then you can print a certificate for the parents. Since the date and ordinance performer are not recorded on the membership record, the parents or someone else will need to provide that information so that the certificate can be created.
Way back when, it was possible to create a record and print the certificate from MLS. If the blessing was performed in another ward, the clerk could specify which ward the record should be moved to. (Well... it was possible except for that one time that I broke it and had to fix it.) Now it is a whole lot easier to have the record created in the ward where the child lives and have that clerk create the certificate.
Pro tip: When someone announces in ward council that a family had a baby, the clerk or executive secretary should take a blank new record form to the parents so that a record can be created and ask the parents if and when they would like to perform the baby blessing. Get the record created so that you aren't discovering years later that you are missing a child in the records.