Split/splitless injector with appropriate split ratio can serve the purpose provided you achieve baseline separation with proper Gaussian shape.  I dont think higher desorption time will help anymore. However, make sure injector should be kept at fiber's operating/ recommended temperature. Additionally, please check the compatibility of injector liner as well.

Good Luck

Hello Anjana -  You can optimize the desorption time by experiment, i.e., inspecting for sample carry-over from previous sample with repeated injection immediately after the original one.  This should be done for some 'worst case' scenarios, e.g., fiber coating with loaded/saturated or loaded with particularly difficult to desorb compounds.  Typically, a splitless mode is used with SPME injections. 

A comprehensive article on SPME method development and troubleshooting of crucial steps is published here:

S. Risticevic, H. Lord, T. Górecki, C. Arthur & J. Pawliszyn. Protocol for solid-phase microextraction method development. Nature Protocols 5, 122-139 (2010). Published online: 7 January 2010.  doi:10.1038/nprot.2009.179.

Good luck with your research,

Jacek

http://www.nature.com/nprot/journal/v5/n1/abs/nprot.2009.179.html

You simply need to set the injector in splitless mode and set the time you want it remain in this mode. After this set time the injector will revert to split mode at a default ratio you have set in the method eg 20:1. Ensure you use a SPME liner with a narrow ID, i.e 0.75mm to get the best peak shapes. If you find that with all this the peaks of interest are very large and not symmetrical then look at either diluting your samples (if liquid) or move to using a split mode rather than splitless at a ratio of say 10:1.

Generally 5-10sec, longer desorption time may cause leaking 

You are right. Purge activation time should be equal or higher than desorption time. Some people study the effect of desorption time and forget to adjust purge activation time (and even forget to provide this important parameter in the article). I typically set purge activation time 1 min higher than desorption time (4 min in your case) and saver activation time 2 min higher (5 min in your case, if used). In this case, I make sure that everything desorbed from the fiber reached the column. When using long desorption times, it is better to keep front of the column cold (40 deg C) during desorption to focus desorbed analytes there.