I THINK the 737s the same as the 777 in that above 1500' RA, APP mode can be deselected by pushing the APP button again.
This puts the AFDS into HDG HLD and V/S, which will then capture the MAP Alt in the MCP.
As a technique, you can THEN press TOGA- retract gear and clean up on schedule, engage HDG SEL or LNAV to follow the lateral path of the MAP.