We would suggest that this year you use a systemic insecticide to reduce the aphid population. Systemic insecticides will be absorbed throughout the plant to kill the feeding aphids. However, if you decide to use the apples, you will need to be very careful to read the manufacturers recommendations for the use of the product and the interval before harvesting crops. It would be advisable to remove the apples this year anyway to give the tree a chance to establish.
In winter use an oil winter wash to remove overwintering aphid eggs. This winter treatment is likely to be most effective at reducing the problem for next year but you will need to be vigilant in spring for a recurrence of the aphid which will need spraying. If the problem recurs next spring you could try using an organic spray. This has quite a short persistence and works on contact so you will need to be thorough and may have to spray several times throughout the season. However, this spray can be used right up to a day before harvesting which is a great benefit.
Globe Artichokes do tend to be prone to blackfly. The most commonly used non-chemical remedy is to spray them with soapy water. You can buy insecticidal soaps but many people make up their own using a teaspoon of washing up liquid diluted in 3 litres of water. The aphids are unable to breath under a coating of soap and subsequently suffocate. If you intend to try this then be sure to spray them on a dull day as spraying in full sun is likely to scorch the foliage.
Other popular methods include squashing groups of them between your finger and thumb or blasting them with a hosepipe to knock them off of the plants. (Be careful not to damage your plants with the pressure of the water.) Annette has also suggested growing other plants as ‘lures’ that are more attractive to the blackfly than the artichokes. Just make sure that you destroy the blackfly when they appear on your ‘lure’ plants, otherwise you will just be increasing the local aphid population! You can spray the lure plants with an insecticide as you are not intending to eat them.