Getting str without HP xp is really only possible through quest rewards, achievement diary rewards, and minigame rewards like Soul Wars and Pest Control.
As KerokeroCola mentioned, the only real way to get strength xp without constitution xp as well is going to be soul wars and pest control which you will have to do things such as heal people and fix barricades so you don't get HP xp while playing aggressive.
Only possible way is through Pest Control or Soul wars, but since you said you're rich...depending on how rich, sell some RSGP and buy some squeal spins. You get a ton of lamps from bought spins it seems.
I play legit and for about 2-4 hours a day. Soul wars takes to long i wish i could buy zeal. Anyways i new i could do soul wars. Im just lazy im lvl 57 with 95 str 99 range. Way to burnt out to continue lol. Guess ill just pk and stake for a bit. Would be nice to max this pure the legit way . Im just a wimp i guess lol.
Why do you want to do it without training HP? After EOC HP will be very important as it doesn't effect combat level. I'd say in preparation for that, you should train regularly to get HP up.
With those stats : 99 range and 95 strength you would make a great pker. Get Mage to 99 too with minimum defense and you'd be a force to be reckoned with in wildy.