It sounds as though you are attempting to remain in Canada. If that is the case I suggest consulting with a Canadian immigration lawyer before coming especially if you’re at planning on claiming asylum. Getting asylum from Nigeria is far from guaranteed and many are denied. Applying for asylum has some pretty serious longterm consequences) not being able to return to Nigeria for over 5 years but often closer to 10, family members struggling to visit Canada or get any form of permit like WP or SP, etc) and being denied asylum has longterm negative consequences (difficultly visiting other countries in the future, difficulty getting WP or SP from other counties, etc.). In terms of your husband’s TRV all you can do is wait. Every person is evaluated individually. If you decide to come to Canada without your spouse and claim asylum it could easily be 3-5 years before you are able to be reunited in Canada but it could be much longer. Unless you have significant savings the government only provides a very small amount of money through welfare which is very difficult to live off of and most have to depend on charity for things like food. It is not advisable to buy a ticket without getting a visa approval first. It will be very difficult to get your passport stamped before June 6th even if you husband is approved. Hopefully they flight is refundable or you can change the dates of the flight.
Are you being invited by family to visit Canada? If you have no connections to Canada it is fairly difficult to get approved to visit Canada as your first trip outside of your own country. Canada is typically not a destination for a first trip abroad because it is expensive and it is very far away. If someone has given you an invitation letter there will be increased scrutiny when it comes to anyone else they may invite because there will be fear that they will try to remain in Canada. This may lead to TRV denials.