Yes, you can inseminate yourself with the donor semen with a needleless syringe. There is no need of liquefy the semen from a fresh donation of the semen. The liquefaction is only done so the semen does not stick to the syringe. But if you use a 10 or 20 ml syringe, which has a wide bore, the semen would not stick to the walls of syringe and would be easily evacuated.
Please feel free for your follow up questions.