Aqui está como fazer o contrário: forçando a execução do cron a usar seu ambiente de login:
bash -lc "your_command"
Do manual do bash:
-c string If the -c option is present, then commands are read from string.
If there are arguments after the string, they are assigned to the
positional parameters, starting with $0.
-l Make bash act as if it had been invoked as a login shell
(see INVOCATION below).
INVOCATION (um pouco despojado):
When bash is invoked as an interactive login shell, or as a non-interactive shell with the --login option, it first reads and executes commands from the file /etc/profile, if that file exists. After reading that file, it looks for ~/.bash_profile, ~/.bash_login, and ~/.profile, in that order, and reads and executes commands from the first one that exists and is readable. The --noprofile option may be used when the shell is started to inhibit this behavior.
Para saber mais: