Yup. We did the same but only needed two channel for either streaming from our phone or blu-ray. Basically you need an HDMI switch where the TV runs to one end and then all the HDMI inputs run into it on the other end. We have an HDMI splitter for the TVs so image will play on both TVs all the time.
Here is a quick picture. We replaced our stock DVD player with a PlayStation for streaming and blu-ray but then the PS4 went out so this is my $5 Good Will player. The 4 channel HDMI switch is the black box and remote