If you really can't do that, use a local password manager like KeepassX on your phone and copy the password by hand on the computer. You compromised only that site. However this can be extremely painful if you use fully random password like g27rkuqhLJcM46G9YsxV4rlF9ACtveB1. These are 32 characters with only letters and digits to limit the typing errors (think about entering punctuation on a very foreign keyboard layout). According to KeepassX its strenght is 191 "quality bits" defined as the "equivalent size of a random symmetric key."
If you use an Internet password manager on an untrusted machine you run into the problem you described and all your accounts are compromised.
By the way, assuming that passwords are stored as SHA-2 (64 characters) should we use 64 characters passwords to minimize the risk of collisions?