Well you are right that Obama is unlikely to provide documentation. As I understand it, he refuses even to release his birth certificate, although that would seem to be a necessary part of the public record to demonstrate that he is constitutionally qualifed to run for president.
I’d also love to see his baptismal certificate. He has said that he is a “member” of Rev. Wright’s church, but that “church” curiously does not require its members to be baptized. So, was Obama ever even a Christian, under the normally accepted meaning of the term? I am not sure if he has explicitly said so, although the press often repeats it, since it might raise difficult issues of Islam and apostasy.
In “Audacity of Hope” he claims explicitly he was baptised, in a curious, passive voice passage notable for it lack of detail.
Given that, as you say, UCC does not mandate baptism for membership, it is quite likely that the ceremony was more like an altar call than a traditional water baptism by immersion or infusion. It is also most likely that the church would not keep special records of any baptism ceremony, if one did occur, only noting that he enrolled as a congregant on a particular date.