How physical do techniques need to be?
The question doesn't really make sense. The only ways I know of to do what you call "non-physical" aikido is in the imagination or in dreams. In the waking world, one has to move, even if no contact is made. Even if a person is not making contact, it's still physical.
If the question is how much strength should be used, the answer is that strength should not be relied on, but rather proper technique, which means aiki. If you don't know what aiki is, then you need to ask your teacher. If your teacher doesn't know, then he shouldn't be teaching aikido and you need to find a teacher that can tell you what aiki is.
There are many high-ranking instructors who still believe that "maximum power" is needed to propery carry out a technique. Such thinking clearly indicates that such individuals have no understanding of aiki. Aiki uses the attacker's power, not nage's. Nage needs to use maximum focus and attention, not "maximum power."
"Maximum power" merely relies on who is stonger and negates the skill of aiki. People who rely on power are generally insecure in their aikido, and rightfully so! They know that there will always be someone who is stronger than them. Their only recourse is to then regress even further back into punching or tripping because they have no skill in aiki.
But people who develop in the way of aiki develop a sense of confidence because they don't rely on strength, which continually deminishes with age, but on skill in aiki, which, through proper training, continually grows with age.
P.S. Admittedly, a certain amount of strength is required for some techniques such as shihonage. A minimum level of grip strength is needed to properly carry out the technique. Grip strength can be developed by practicing about 200 overhead cuts with a bokken on a daily basis.