The new building is listed under "Works Completed" in the PWD's Annual Report for 1928:
School—“Ying Wah College”—on K.I.L. 1784, Bute Street and Sai Yeung Choi Street, Mong Kok Tsui.
The history page on the school's website says the school moved to new premises on Oxford Road in 1963:
Student enrollment started to rise and the premises at Bute Street were proved too small. In the summer of 1963, the new college building at Oxford Road was opened with substantially improved facilities, but the primary section had to be closed.
I'm not sure if this building was demolished immediately after the school moved out, or if it was used for other purposes for some time. Phil's comment below shows the building was used by the Church of Christ in China until it was demolished in November 1994.
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Green Building
There's an image on Getty from SCMP that was taken in 1994 and the caption attached to it mentions the old building (then occupied by CCC and known as the "Green Building") at 56 Bute Street was due to be torn down that November. It doesn't state when CCC moved into the premises though, but at least it appears the building remained for afew more decades before demolition.