With a white vehicle, you could run naked as chips won't show as readily compared to dark color cars. But, they are very beneficial for preventing area from getting messed by front wheel sling - particularly if you AX, DE, or drive where there are lots of loose stones. So, replacing is best bet and inexpensive as I recall.
A number of 997 owners have gone retro and refreshed w/ matte black guards (
ebay example here) and in some instances it looks really good. On my 997 I had installer replace w/ Xpel clear and oversize new ones a bit based on wear marks outside originals.
You can DIY as area does not have a complex surface or have a decent local clear bra installer do for you in ~ 30-45min. If DIY, use a heat gun (prefered) or hair dryer on low setting to heat film to aid in removal - but pull back very slow and evenly. Hit up youtibe for some quick instructions. Then clean remaining residue w/ an IPA solution and to prep area. Install new according to mfg. I'm sure there are some Boxster/Cayman kits on eBay if you want to DIY.
Good luck
PS - Advances in film material relative to ones currently installed on your car is amazing. New stuff (especially Xpel) has virtually zero orange peel and guarantee against yellowing for upto 10 years. One tip is to NOT use any yellow carnuba wax on the film. Instead use a synthetic polymer blend as I'm told (and has worked for me thus far).
PPS - I've had some success cleaning yellowed film up too. Use Blue Coral metal polish (yes metal). Basically it strips oxidized top layer away which you then use a fine polish on to get back to gloss. Seal w/ a synthetic wax/protectant.