Can we crucify the old Adam ourselves?
No, the old Adam cannot be crucified by human effort; it is wholly and completely a work of God. Crucifixion was chosen because a person cannot crucify himself—cannot drive the nails or raise the pole—so this death must be done by outside action.
Les explains from Romans 7:5 that Paul is dealing with breaking the relationship of old Adam, who has to be crucified, not by anything we do. We cannot crucify ourselves. Crucifixion was chosen rather than any other form of death because it is one form of death man cannot accomplish on his own; you cannot drive the nails into your hands and put the pole up in the air, because that had to be done by outside. So as we are crucified with Christ, it is nothing we can do—it is totally, wholly, and completely a work of God on our behalf. Les also notes that verse 5 reviews being in the flesh under old Adam's control, producing the motions or results of sins, plural. Sin is old Adam, the fountainhead and manufacturing point of our sins, while what we do are sins, plural.
For when we were in the flesh, the motions of sins, which were by the law, did work in our members to bring forth fruit unto death.