Bismillahir Rahmanir Rahim.
Wa'laykum-as-Salaam wa Rahmatullahi wa Barakaatuhu.
This maslah that you have stated, that your salaah is invalid, according to Hanafi Fiqh, in a non-Islamic state is untrue. However, if there is proof to the contrary, then I would like to see this.
The issue concerning Jumm'ah salaah which has a few conditions, some of them which we shall identify are as follows:
a) It must be within a town or city, in which there are a reasonable amount of people populated. By city we mean an area of streets and roads, which has a bazaar/shops, a police station, a graveyard etc.
b) It must have a king/Sultan or his deputy, whom he has ordered to perform the Jumm'ah
c) The time for the Jumm'ah prayer must be that of the Zohar Salaah.
d) The Friday Sermon (khutbah), which must be before the congregational prayer (jamaa'ah), and must be in front of a certain number of people to which there is no limit.
e) Apart from the Imam there must be at least three people present. If there are only women and children, then it will render the Jumm'ah invalid.
These are the conditions for a Jumm'ah to take place.
I think the questioner may have got the question mixed up in having the performance of Jumm'ah in a non-Islamic state, and the performance of a Jumm'ah where there is a Sultan/king or deputy present, therefore I shall discuss the possibility of a Jumm'ah according to Islamic principles even in a non-Islamic state.
As far as Salaah is concerned, then it is our belief that the Messenger of Allah (peace be upon Him) had performed the Salaah, even though it had been prescribed at a later stage. Examples of this can be seen in Tafsir-e-Na'imi by Mufti Ahmad Yar Khan Na'imi, under the verse
'Subhaan alladhi asraa bi 'abdi hi laylam minal Masjid il Haraami ilal Masjidil Aqsa'
Which is in the fifteenth chapter of the Noble Qur'an.
By having a Sultan/king or deputy, then there does not seem to exist the formewr two, yet thier deputies, or indeed the deputies of the Messenger of Allah (peace be upon Him) do exist. They are the scholars ('ulama'). They must fully comply with the Sunnah and the shari'ah, and not be shaven/half shaven wearing suits or praying the sermon (khutbah) in English.
After, the revelation had been given to perform salaah i.e. the Jumm'ah Salaah which was
'idhaa nudiya lis salaati miy yawmil Jumu'ati fas'aw ilaa zikrillahi wazarul bay',
then according to the books of sirah, there were Jumm'ahs conducted in certain places like Yemen, although they did not have an Islamic governor. Similarly, we do not have an Islamic government in England, America, Australia, New Zealand and elsewhere, yet we still perform the Jumm'ah prayer, so that we do not contravene the Qur'an and the Sunnah, by non-performance.
Therefore it is our duty in Islam (fard), to conduct the Jumm'ah prayer, in the Ja'me'ah Mosque of a town or city, and not deprive ourselves of its non-fulfilment. The above conditions were merely guidelines by the Hanafi scholars at a time when Islam was flourishing, and there was no thought of Muslims being inhabited in non-Islamic states, therefore Jumm'ah is very important, to the extent that it has more stress than the Zohar prayer. It is a 'Fard-e-'ayn' and the denier of it will be out of the folds of Islam!
May Allah the Almighty keep us firm on the five time prayer including Jumm'ah, and may he keep us away from all forms of oppression, tyrrany, and depression.
Wa ma tawfiqi ilaa Billahi,
M. Waseem Ashrafi.