How to cope with a resistance of an inductor ?

I totally agree about just wiring it up if you already have this inductor, and also with what sreten said. The only mistake would be to go out and order a new high-DCR inductor specifically for this purpose when you could get a more appropriate one for much less money anyway. That said...

Since the magnitude, frequency, and importance of the DCR influence depends on the impedance/cabinet and response of the actual woofer used, I don't see much value in simulating a different woofer and different cabinet. Yes, differences will probably be <2dB, as they are in that sim, but when you're trying to make a 3-6dB change, 2dB is kind of a problem.
 
If you use that inductor, your bass response will change due to the high resistance, and you will have a fair amount of insertion loss. Qes and Qts both increase with added resistance in the inductor.

If the bass response change is not a deal breaker, and you liked the woofer/tweeter balance before, you will want to pad down the tweeter by whatever the insertion loss is in addition to the change required by your shelving filter.
What dB gain I will see on my woofer (1st order crossover) if the DCR from my series inductor is changed from 0.92 ohm to 0.15 ohm ? The driver is 8 ohm rated Hivi B4n.