How do I test to see if an application exists in $PATH?

I’m trying to write all of my sh startup/env scripts to work with as much DRY and as much: “works on every *nix I clone it to”, as possible. This means making sure that if I try to run code that’s not there, that the code fails gracefully. To that end I need to be able to test if programs exist. I know how to test if a file exists, but I’m not sure how to test to see if an application is executable within the path. I’d rather use the $PATH, as some of these need to work on arch, ubuntu, and centos. Some might be installed in my homedir, on systems where I don’t have root, others might not be installed, and others yet my be installed in system paths.

Choose interpreter after script start e.g. if/else inside hashbang

Is there any way to dynamically choose the interpreter that’s executing a script? I have a script that I’m running on two different systems, and the interpreter I want to use is located in different locations on the two systems. What I end up having to to is change the hashbang line every time I switch over. I would like to do something that is the logical equivalent of this (I realize that this exact construct is impossible):