Is it secure to choose d in a RSA key pair?
Selecting a small $d$ is known to be insecure.

Wiener has shown in 1990 that if $\log d \leq \frac14 \log N$, the private exponent $d$ can be reconstructed from the public key $(N,e)$.

If you're interested in making the private computational cost cheaper, then I would suggest that RSA is not the best solution; I would recommend you start looking at Elliptic Curve based solutions.