Short answer: Do not perform abhishek on the teerthankar idol while your finger is cut and bleeding. Focus on stopping the bleed and maintaining purity; when you are clean and free of bleeding, you may resume worship as usual.

Reasoning in Jain practice:

• Abhishek and temple puja are sacred activities that require cleanliness and purity. If you are bleeding, there is impurity (mala) from the injury, and touching the idol with blood is not appropriate.
• First, stop the bleeding, wash and clean the wound, and keep the area covered to prevent further contamination.
• Once your wrist/hand is clean, bandaged, and free of blood, you can perform the ritual with proper hygiene, or continue with silent prayer, meditation, or reading/sadhana if you cannot perform the full abhishek at that moment.
• If the wound is minor and you cannot avoid engaging in worship, you may choose to offer fruits, flowers, or recite mantras in a clean, respectful manner from a short distance, until you are fully clean.

Practical steps you can follow now:

• Rinse and lightly scrub the wound with clean water; apply a clean bandage.
• Wash your hands before touching any idol or puja items.
• When ready, perform abhishek with purity and calm, avoiding use of impure liquids or substances if you are not fully clean.

If you want, I can look for specific guidance from Jain sources to quote or cite exact passages.