(Wiener) deconvolution with high resolution kernel

Given the system y(t) = (h * x)(t) + n(t)

I have 1D data y(t) which is sampled at a relatively low temporal resolution. The sampling rate of this signal cannot be improved due to technical limitations. The impulse response h(t) follows a model which is known at a much higher temporal resolution. When using Wiener deconvolution to obtain x(t) I would need to resample h(t) at the sampling rate of y(t). Is there a way to improve the estimate of x(t) at low temporal resolution by using h(t) at high resolution?