Okay, running in CS:S is a hold to toggle command, and you want to convert it to a push to toggle.
First, go into console and type:
bind "THEKEYTHATTOGGLES" - write down the command it gives. It should be +something. This is key.
Create a blank text file for this, and call it running.cfg or something.
In it, put this in:
alias "movefast" "+something; bind KEY moveslow"
alias "moveslow" "-something; bind KEY movefast"
bind "KEY" "movefast"
In your CS:S directory, you should have an autoexec.cfg. In it, put the following:
exec running.cfg
This converts running into push once to move slow, push again to move fast, and will execute upon entering a game, thus ensuring it is bound to a key. However, I don't trust the autoexec.cfg, so we're going to do another change.
Open your config.cfg, and add the following line at the bottom:
bind "KEY" "movefast"
Close, run CS:S, bring down console, type in:
map "MAPNAMEHEREOMGIDONTPLAYCSSOYOUHAVETOFIGURETHISOUTYOURSELFMAN"
Once map loads, exit, and check to make sure the key bind for "movefast" is still in your config.cfg. Mark your config.cfg read-only - provided the settings in it are one's you'd like to keep for a while.
Edit: You can substitute "movefast" for "moveslow" in the bind line depending which way CS:S defaults you. i.e. if you WALK by holding the key, you can change the bind command.