The CurveFitter App is simply not designed to be used in this manner.
To do this, you would create a fit object directly with the <cfit> function and set the model and coefficients in the object fields and then use <feval> to evaluate the model over the input points.
Of course, when you do this, then the fit object will not have any of the supporting data available to it for confidence limits, goodness of fit, etc., etc., ... that are automagically populated when the fit function is called and creates the output fit object. You would have to derive all those from the results of the residuals and data points and, of course, there's no guarantee that these will be at all representative of the estimated values would obtain by fitting the model so there's no real justification for anything other than computing the residuals and basic global measures of goodness of fit like R-square or the standard error.
Depending upon the model, it may be simpler to just write an evaluation function directly as an m-file or anonymous function.
