Hello Hawaiian Dreams I just spotted your post. To answer your question about sending distant reiki without the use of the symbols, I believe yes you can, for example, when I first became attuned to reiki level one, I was asked to send some healing to a friend, All I had was this person's name and location, obviously I did not have any symbols in sending the reiki, just my intention to send it I believe was enough and when I asked my friend they had received it.
After all it is all about intention as my reiki masters told me. Even still now I don't always use the symbols if I am in a desperate need to send healing.
Love GA x