The use of ASM module will not handicap performance of LTM module. What will be affected is the overall performance of your application (page load time). As a rule of thumb, expect at least 15% increase in page load times due to ASM security-checks. If you use poorly configured policies (i.e. apply 'All Signatures', and enable all blocking settings that some do), this performance loss will be greater.
2200s Appliance only has 8GB memory, but with optimized configurations, you can pull off LTM + ASM in low-activity environments. To make a judgement call if you can provision ASM without taking great capacity risks, have a look at your performance graphs. What is your current CPU and Memory usage during peak-activity hours?