How to design a delay and sum beam former with fractional delay less than one sample?
There is no reason you cannot use exponential weights. Those are used in the frequency domain, not in time domain, and won't produce imaginary part.  

Using the Translation/ Time-Shifting Property of the Fourier transform, you can define the weights (per frequency bin), even for fractional delay. By the way, the problem of fractional delay is not only when it is less then 1 sample. Flooring all delays to be integers will produce sub-optimal results.  

A different approach is to use interpolation in time-domain to obtain values between samples, e.g. using interp1. This approach will be much slower, if it matters.