One of the ways...
Consider that different machines may need different paths and may have different shell (bash, dash, sh, csh, tcsh, zsh...) and the command/alias of one can be not adequate or understandable for the others.
It is already a good practice to have a
.bash_aliases file in which to put your commands and to copy that file on the remote machines, but it seems to be what you do not want to do
So you can think to something like to put your alias or the commands you want to execute in a file (e.g.
remote-box-commands.bash) then to do on the local machine
cat remote-box-commands.bash | ssh user@remoteserver
and in the file
remote-box-commands.bash you put something like
#Put here your ~/.profile # or the command you want to execute remotely
/bin/bash # or whatever shell you will use.
You should complete with the proper options.
For the help on whatever command use
man whatever or
help whatever (if internal of the shell).
Read more for examples here