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In most applications, you have to scale your ground motions per a well-recognized scaling technique.  Generally, the contribution of seismic isolation is pronounced in the case of severe ground motions. On the other hand,  seismic isolation has no contribution in the case of very weak excitation. So you need to avoid the use of weak and strong ground motions.  You can manage your study to consider multiple hazard levels (for example 10% – 10 years and 2% – 10 years)  to shed light on the dependency of the seismic isolation to ground motion intensity. Note, quasi-static loading might work for some vibration controllers, such as displacement-dependent dampers,  but their application makes no sense in the case of a base-isolated system. Better you research and get to a conclusion.

Actually, as much as I have encountered in research and guidelines, there are very few applications of time history analysis without a proper scaling of records, because generally original records of strong ground motions are not able to demonstrate capacities and critical behaviours of structures against earthquakes. So, it may be proper to consider a specific hazard level and scale ground motion records to meet a certain intensity. Besides, I suggest you are better to select records which average of their spectral shape has an acceptable consistency  with a specific acceleration spectra (there are methods approved by codes to develop acceleration spectra special for near field zones).  This way your results will be more consistent and useful.

The document, written by distinguished professor of the University of California, Berkeley,  Prof Anil K. Chopra is a very relevant source and you may find it useful. “Practical Guidelines to Select and Scale Earthquakes.” The objective of this report is to develop a “new practical method for selecting and scaling earthquake ground motion records”  in a form convenient for evaluating existing structures or proposed designs for new structures. The selection procedure considers the important characteristics of the ground motions (e.g., pulse, directivity, fling, basin, duration etc.) consistent with the hazard conditions. The scaling procedure represents explicitly considering structural strength and is based on the standard IM of spectral acceleration or  it can be computed from the uniform hazard spectrum obtained by probabilistic seismic hazard analysis (PSHA) for the site. Hope, this information might be useful as a reference