Not sure which some parts of South Africa you are referring to as in the Act no crossbows are permitted for hunting in South Africa.
You might be able to apply for a special permit(if you can motivate why you want to use a crossbow) from the Nature conservation authorities in the province you intend hunting before arriving on your hunt.
One of the limitations is the minimum length of the arrow which has to be 19.68 inches, many crossbow arrows are shorter.
NATIONAL ENVIRONMENTAL MANAGEMENT: BIODIVERSITY ACT, 2004 (ACT NO. 10 OF 2004)
No.34326 GOVERNMENT GAZETTE, 27 MAY 2011
NORMS AND STANDARDS FOR HUNTING METHODS IN SOUTH AFRICA
Permissible bows for bow hunting
6. The following are acceptable types of bows for bow hunting-
( a) longbow;
(b) recurve bow; and
(c) compound bow.
Minimum requirements for bow hunting
7. 1) The minimum requirements to hunt specific categories of wild or allen animals by means of
bow and arrow are the following-
a) For wild or alien animals of a small size. including gamebirds, small carnivores, hares, hyraxes,
rabbits and pygmy antelope, the-
i) kinetic energy should not be less that 30ft/lbs; and
ii) arrow weight should not be less than 300 grains;
(b) For wild or alien animals of medium size, including reedbuck, impala, blesbuck, warthog, bushpig,
springbuck and nyala, the-
i) kinetic energy should not be less that 50ft/lbs; and
ii) arrow weight should not be less than 380 grains;
(c) For wild or allen animals of large size, including wildebeest kudu, gemsbuck, zebra, waterbuck,
sable and hartebeest, the-
i) kinetic energy should not be less that 60ft/lbs; and
ii) arrow weight should not be less than 415 grains;
(d) Cape buffalo, the-
i) kinetic energy should not be less that 80 ft/lbs; and
ii) arrow weight should not be less than 750 grains; and
(e) Giraffe, the-
i) kinetic energy should not be less that 90ft/lbs; and
ii) arrow weight should not be less than 750 grains.
(2) In addition. to the requirements contemplated in sub-paragraph (1) the following conditions
apply with regards to the use of mechanical broad heads-
( a) for species contemplated In sub-paragraphs (1)(a), (1)(b) and (1)(c), 5% additional kinetic energy is
required;
(b) broad heads must have at least two cutting edges; and
(c) the minimum permitted arrow length is 50cm.