You are right to be wary. For me the primary purpose of the hand jammer safety cord (shock cord) is to resist a fall with reasonably impact loading. Fall onto hand jammer is foreseeable when clambering at pitch head, fall whilst swapping over chest jammer at rebelay, chest jamer slips or opens, bolt failure. Any of these falls could easily happen at pitch head or near anchor therefore pitch rope is not guaraneed to be available to absorb the impact. So a fall is foreseeable and it is possible there will be little other shock-absorbing material in the system, increasing the shock load on you, your jammer, the remaining rope and the anchor. Here some stretch is a big benefit in reducing impact and therefore peak force.
A 'non-stretch' safety cord does not seem to provide any advantage as this is not loaded in normal use for progression, such as footloops are. (NB static footloops made of dyneema are not expected to resist a shock load in normal use).
So whilst dyneema safety cord might be strong enough, it would not provide much shock absorbancy in event of fall which is its primary purpose so this is a major disadvantage. Whether this is 'safe' is for you to decide, but on this count alone it defintely seems less safe than the conventional rope option.
If you wish to persue a low-bulk kit, there are several alternatives worth considering. Simplest is perhaps just to swap your existing safety cord (i dont know what this is made of) for thin (8/9mm??) safety cord. This could be 'static' caving rope (better stretch than dyneema and cheap and easily integrated with footloop) or dynamic climbing rope (better stretch still).
Extending the dynamic safety cord idea, you probably already carry dynamic rope in the form of cowstails, so could eliminate the safety cord altogether and simply clip hand jammer with a cowstail. Good shock absorbancy and zero bul. But potential for fortgetting and/or dropping jammer. This method is described in Alpine Caving Techniques, which is well worth a read for other SRT/rigging ideas.