* Belt Routing: The serpentine belt's routing is determined by the presence of all the driven components (alternator, power steering pump, water pump, AC compressor). Removing the AC compressor changes the routing significantly. You'll need a new, shorter serpentine belt specifically designed for a 1988 Cadillac *without* air conditioning. You can't just use any shorter belt; the belt's length and the number of grooves must be correct to avoid belt slippage, premature wear, or component damage.
* Finding the Correct Belt: You'll need to find a replacement belt specifically for a 1988 Cadillac without AC. This might require checking a parts store catalog using your Cadillac's VIN or engine code, or consulting a repair manual. The wrong belt length can damage the components it drives.
* Compressor Removal: You'll need to physically remove the AC compressor and its associated mounting brackets. This is a mechanical task and will involve some tools and potentially some refrigerant evacuation if you're not already low on refrigerant. Leaking refrigerant is harmful to the environment.
* Potential Idler Pulley Issues: In some cases, the AC compressor may have acted as a tensioner or have had a related idler pulley. Removing it might require a different pulley setup or adjustment. This is often addressed by using a special bypass pulley.
In short, while it's *possible*, simply removing the compressor and putting on a shorter belt is likely to lead to problems. You should obtain a replacement belt designed for your specific Cadillac model *without* air conditioning. You might also need to obtain a bypass pulley depending on your model. Consulting a repair manual specific to your 1988 Cadillac's engine is highly recommended to understand the correct belt routing and any necessary additional parts.