There the way to do it in Electrum even if your mSigna isn't synced, but you must have a list of your addresses.

Here's how to do it:

• Create an Electrum wallet with the option "Import bitcoin address or private keys" and paste ALL of your addresses with transaction history, including the empty ones (if unsure, just paste all).
• Finish creating the wallet and let Electrum Sync.
• Go to History tab and you should see a list of transactions.
• Now, each transaction should be imported to mSigna manually, from old to new: to do that, open a transaction history in Electrum through "Right-Click->Details".
• In the transaction details, export it via "Share->Copy to Clipboard".
• In in your mSigna wallet, click "Transactions->Import Transaction->From Clipboard (raw)" and it will be added to your Transactions tab.
• Do that t the rest of the transactions in Electrum to manually sync your mSigna wallet.

After importing all of the transactions, just create a transaction manually, export it (raw) and import it to Electrum to broadcast.
Here's the detailed steps to Send the transaction:

• In mSigna, Go to 'Accounts' tab; click the correct account and then click "Send".
• In the Send window, Tap "Enable Coin Control" for easier manual txn generation.
• Select all of the available inputs and the total should be listed below.
• Set an absolute fee (it's not fee rate) which should be not less than the standard fee for the transaction's size.
• Now fill up the address and amount which should be equal to the fee deducted from the inputs' amount.
• Click Sign to finalize it (or "Save Unsigned->Right click on the created unsigned txn in the history->Signatures...->Right-Click->Add Signature").
• Now to Broadcast that Signed Raw transaction, right-click on it and select "Export Transaction->To Clipboard (raw)"
• Import it to Electrum via "Tools->Load transaction->From text", then click broadcast.