I run my 7300 and 9700 off of 1 switching PSU. There are many varieties out there that will suffice (30A with 35A surge). No way I am going to key up both at the same time. But that's just me.
Unless you plan to transmit with both of your radios simultaneously, that power supply should do OK. Looks like that PS is sold by Martin Lynch and I found an owner's manual. It's rated for 20 amps continuous. The IC-7300 is rated to draw 21 amps at full power, but most run a little short of that.