Hi, Sorry to hear about the breakdown of your marriage.
Try not to stress yourself out too much about this. There are steps that your solicitor can take in order to progress your divorce.
It sounds like your solicitor has out of courtesy, send him a copy of the proposed particulars of unreasonable behaviour prior to the issue of the petition, which is always preferable. This gives a chance for you to negotiate with regards to the allegations of his behaviour. Sometimes it can just be one particular allegation that respondents don't like and it can be agreed to amend/tone down the allegations, as long as there is still enough there to satisfy the Judge that the marriage has irretrievably broken down.
If the petition has not yet been issued in the Court, then this would be your best course of action. Even if it has been issued, if there is something that may cause your DH to defend the divorce or cross-petition then potentially you could amend the petition although this would involve more costs (Court fees and additional work by your solicitor) and a delay.
By him saying he will say you cheated on him this could mean that he is thinking of cross-petitioning. This means that he would also issue a petition (on your adultery by the sounds of it) but he would need evidence of this if you are not going to admit it. To be honest, this is a pointless (and costly) exercise as bottom line, the divorce will still go through on one petition, either yours or his and it makes no difference to anything else (ie finances/children) whose petition goes through.
Worse case scenario he could say he wants to defend the divorce and say that the marriage has not irretrievably broken down. Again, a pointless and VERY expensive exercise and I imagine that if he went to see a solicitor and instructed them to do this they'd want a serious amount of money up front (at least £1,000). Defending a divorce is simply a delaying tactic and ultimately it will go through. He would almost certainly be ordered to pay your (wasted!) costs too.
Good news is he can't afford a lawyer which means he is unlikely to challenge anything.
He is obviously pissed off about something in the particulars so in my opinion I would talk to your solicitor about perhaps toning down the particulars or amending them in someway, ensuring there is still enough to satisfy the DJ that the marriage has broken down.
If he doesn't sign the papers, then there is a way to proceed. Your solicitor will need to instruct a process server(private investigator) to serve him personally with the papers. He or she will then prepare an affidavit (statement) setting out that the respondent (your DH) has been served and your solicitor will use a copy of this affidavit to exhibit to your affidavit in support of petition which is the next stage in the divorce proceedings.